xSMZ2 c.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy\n",
    "from scipy.integrate import solve_ivp\n",
    "import scipy.integrate as integrate\n",
    "from scipy.optimize import fsolve\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set_style(\"white\")\n",
    "from scipy.interpolate import splev, splrep\n",
    "from scipy.interpolate import InterpolatedUnivariateSpline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The critical temperature, TC:  125.212\n",
      "Value of phi at TC:  172.832\n",
      "The \"zero\" temperature, T0:  109.25166194810522\n",
      "vC/TC:  1.380310693272699\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# T = 0 masses\n",
    "mW0 = 80   #W boson mass\n",
    "mZ0 = 91  #Z boson mass\n",
    "mh0 = 125   #Higgs mass \n",
    "v0 = 246.0    #Higgs VEVss\n",
    "mt0 = 173   #Top quark mass\n",
    "lambdaH = mh0**2/(2*v0**2)  # lambda\n",
    "\n",
    "mS2 = 550**2\n",
    "lambdaHS = 3.9\n",
    "muS2 = mS2 - lambdaHS*v0**2\n",
    "mH2 = mh0**2/2\n",
    "muH2 = -mH2\n",
    "\n",
    "# Coefficients in eq (213)\n",
    "D = (2*mW0**2 + mZ0**2 + 2*mt0**2)/(8*v0**2) \n",
    "E = (2*mW0**3 + mZ0**3)/(4*np.pi*v0**3) \n",
    "B = 3/(64*np.pi**2*v0**4)*(2*mW0**4 + mZ0**4 - 4*mt0**4)                \n",
    "Tmin2 = (mh0**2 -8*B*v0**2)/(4*D)\n",
    "\n",
    "\n",
    "def lTemp(T):\n",
    "    lambdaTemp = - 3*(2*mW0**4*(np.log(mW0**2/T**2) - (5.4076- 1.5))\\\n",
    "                    + mZ0**4*(np.log(mZ0**2/T**2) - (5.4076 -1.5)) - 4*mt0**4*(np.log(mt0**2/T**2) - (2.6351 -1.5)))/(16*np.pi**2*v0**4)\n",
    "    return lambdaH + lambdaTemp\n",
    "\n",
    "phi = np.linspace(0, 350, 100)\n",
    "\n",
    "def potentialQ(phi, T):\n",
    "# Potential given by (213)\n",
    "    return D*(T**2 - Tmin2)*phi**2 - E*T*np.abs(phi)**3 + lTemp(T)*phi**4/4\n",
    " \n",
    "def potentialHiggs(phi, T):\n",
    "    #Quantum and thermal loop corrections from Higgs \n",
    "    massHiggsField = 3*lambdaH*phi**2 - mH2\n",
    "    thermal = (1/24)*massHiggsField*T**2 - (np.abs(massHiggsField)**(3/2)*np.sign(massHiggsField))*T/(12*np.pi) - 1/(64*np.pi**2)*massHiggsField**2*(np.log(mh0**2/T**2) - (5.4076 -1.5))\n",
    "    quantum = 2*mh0**2*massHiggsField/(64*np.pi**2)\n",
    "    return thermal + quantum\n",
    "\n",
    "def potentialSinglet(phi, T):\n",
    "    #Quantum and thermal loop corrections from Singlet\n",
    "    thermal = (muS2 + lambdaHS*phi**2)*T**2/24 - (muS2 + lambdaHS*phi**2)**(3/2)*T/(12*np.pi) - 1/(64*np.pi**2)*(muS2 + lambdaHS*phi**2)**2*(np.log(mS2/T**2) - (5.4076 -1.5))\n",
    "    quantum = 2*mS2*(muS2 + lambdaHS*phi**2)/(64*np.pi**2)\n",
    "    return thermal + quantum\n",
    "\n",
    "def potential(phi, T):\n",
    "    sm = potentialQ(phi, T)\n",
    "    h = potentialHiggs(phi, T)\n",
    "    s = potentialSinglet(phi, T)\n",
    "    return sm + h + s \n",
    "\n",
    "\n",
    "def dVdphi(phi, T, phiTest=None):\n",
    "    # Derivative of the potential w.r.t phi\n",
    "    pot = potential(phi, T)\n",
    "    spl = InterpolatedUnivariateSpline(phi, pot)\n",
    "    splder = spl.derivative()\n",
    "    # If we want the derivative at a specific value provide phiTest and return the derivative at that point\n",
    "    if isinstance(phiTest, float) or isinstance(phiTest, int):\n",
    "        der = splder(phiTest)\n",
    "\n",
    "    else:\n",
    "        der = splder(phi)\n",
    "    #print(\"dVdphi: \", der)\n",
    "    return der\n",
    "\n",
    "def dVdT(phi, T):\n",
    "    # Derivative of the potential w.r.t T\n",
    "    quiros = 2*D*T*phi**2 - E*phi**3\n",
    "    massHiggsField = 3*lambdaH*phi**2 - mH2\n",
    "    higgs = massHiggsField*T/12 - (np.abs(massHiggsField)**(3/2)*np.sign(massHiggsField))/(12*np.pi)\n",
    "    massSingletField = muS2 + lambdaHS*phi**2\n",
    "    singlet = massSingletField*T/12 - massSingletField**(3/2)/(12*np.pi)\n",
    "    logTerms = (2*3*(2*mW0**4 + mZ0**4 - 4*mt0**4)/(16*np.pi**2*v0**4))/T + 2/(64*np.pi**2)*(massSingletField**2 + massHiggsField**2)/T\n",
    "    derT = quiros + higgs + singlet + logTerms\n",
    "    return derT\n",
    "\n",
    "def equations(x, phi):\n",
    "    # The critical temperature is when we have a degenerate minimum, i.e dVdphi = 0 and V = V(phi_F).\n",
    "    # Hence define a system of non-linear equations with V - V(phi_F) = 0 and dV/dphi = 0 \n",
    "    phiMin, T = x\n",
    "    Vfalse = potential(0, T)\n",
    "    V = potential(phiMin, T) - Vfalse\n",
    "    dV = dVdphi(phi, T, phiTest=phiMin)\n",
    "    return [V, dV]\n",
    "\n",
    "# Use fsolve to find the roots of the system of equations\n",
    "# Use the last point of the span of phi as an initial guess to find the right minimum, not phi_F = 0\n",
    "phiAtMin, TC = fsolve(equations, [phi[70], 120.0], args=(phi,))\n",
    "print('The critical temperature, TC: ', np.around(TC, 3))\n",
    "print('Value of phi at TC: ', np.around(phiAtMin, 3))\n",
    "\n",
    "def findT0forVEV(t):\n",
    "    dV = dVdphi(phi, t, phiTest=v0)\n",
    "    return dV\n",
    "\n",
    "T0, = fsolve(findT0forVEV, TC)\n",
    "print('The \"zero\" temperature, T0: ', T0)\n",
    "\n",
    "def findPhiMin(phiMin):\n",
    "    phiMin = phiMin[0]\n",
    "    dV = dVdphi(phi, T, phiTest=phiMin)\n",
    "    return dV\n",
    "\n",
    "def findPhiForTN(phiN):\n",
    "    phiN = phiN[0]\n",
    "    dV = dVdphi(phi, TN, phiTest=phiN)\n",
    "    return dV\n",
    "\n",
    "def latentHeat(TN, phiN):\n",
    "    rhoR = 106.75*np.pi**2*TN**4/30\n",
    "    VEW = potential(phiN, TN)\n",
    "    VF = potential(0, TN)\n",
    "    dVEWdT = dVdT(phiN, TN)\n",
    "    dVFdT = dVdT(0, TN)\n",
    "    alpha = (VF - VEW + TN*(dVEWdT - dVFdT))/rhoR\n",
    "    return alpha\n",
    "\n",
    "# TN = 116.9\n",
    "# phiN, = fsolve(findPhiForTN, phiAtMin)\n",
    "# print('Phi at TN: ', phiN)\n",
    "# print('vN/TN: ', phiN/TN)\n",
    "\n",
    "potentialTC = potential(phi, TC)\n",
    "# potentialTN = potential(phi, TN)\n",
    "potentialT0 = potential(phi, T0)\n",
    "\n",
    "# alpha = latentHeat(TN, phiN)\n",
    "# print('Latent heat: ', alpha)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(phi, potentialTC, label=('T$_C$'))\n",
    "#plt.plot(phi, potentialTN, label=('T$_N$'))\n",
    "plt.legend()\n",
    "plt.xlabel('$\\phi$ [GeV]')\n",
    "plt.ylabel('$V(\\phi, T)$ [GeV$^4$]')\n",
    "plt.ylim([3.6e7, 4e7])\n",
    "plt.xlim([0,260])\n",
    "sns.despine()\n",
    "\n",
    "# plt.figure()\n",
    "# plt.plot(phi, potentialTC, label='TC')\n",
    "# #plt.plot(phi, potentialTN, label='TN')\n",
    "# plt.plot(phi, potentialT0, label='T0')\n",
    "# plt.legend()\n",
    "# plt.xlabel('$\\phi$ [GeV]')\n",
    "# plt.ylabel('$V(\\phi, T)$ [GeV$^4$]')\n",
    "# plt.ylim([-7e7, 4e7])\n",
    "\n",
    "# phi2 = np.linspace(-350, 350, 100)\n",
    "\n",
    "# potentialSym = potential(phi2, 2*TC)\n",
    "# potentialBroken = potential(phi2, T0)\n",
    "\n",
    "# plt.figure()\n",
    "# plt.plot(phi2, potentialBroken, label='EWSB')\n",
    "# plt.plot(phi2, potentialSym, label='Sym')\n",
    "# plt.legend()\n",
    "# plt.xlabel('$\\phi$ [GeV]')\n",
    "# plt.ylabel('$V(\\phi, T)$ [GeV$^4$]')\n",
    "# plt.ylim([-7.5e7, 7.5e7])\n",
    "\n",
    "# der = dVdphi(phi, TC)\n",
    "# plt.figure()\n",
    "# plt.plot(phi, der)\n",
    "# plt.ylim([-4e5, 4e5])\n",
    "# plt.xlabel('$\\phi$ [GeV]')\n",
    "# plt.ylabel('$dV(\\phi, T)/d\\phi$ [GeV$^4$]')\n",
    "# #plt.xlim([0,250])\n",
    "# plt.title('Derivative of V w.r.t $\\phi$')\n",
    "# # #print(potentialTC)\n",
    "\n",
    "print('vC/TC: ', phiAtMin/TC)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def equationsBounce(r, y, temp, phi):\n",
    "    \"\"\"\n",
    "    Function setting our equation system from the EOM of the bounce. \n",
    "    Turning equation of 2nd order ODE, to system of two 1st order ODEs.\n",
    "\n",
    "        From: dphi^2/dr^2 + (alpha/r)*dphi/dr = dV/dphi\n",
    "\n",
    "            introduce v = dphi/dr, s.t dv/dr = dphi^2/dr^2\n",
    "            and then y = [phi, v], dy/dr = [dphi/dr, dv/dr]\n",
    "\n",
    "        To: dy/dr = [dphi/dr, dv/dr] = [v, -(alpha/r)*dphi/dr + dV/dphi]                                              \n",
    "\n",
    "    @param r: For T=0, r = sqrt(t^2 + x^2), for finite T r = r\n",
    "           y: Array of phi and dphi/dr\n",
    "           alpha: D-1 term, equals either 3 in 4D or 2 in 3D\n",
    "    @return dydr: Array of dphi/dr and dphi^2/dr^2\n",
    "    \"\"\"\n",
    "    # Pick out the values from y = [phi, v]\n",
    "    h = y[0]\n",
    "    v = y[1]        # v = dphi/dr\n",
    "\n",
    "    #print(\"Phi: \", phi, \"Temperature: \", temp)    \n",
    "    # Finite-T\n",
    "    alpha = 2\n",
    "\n",
    "    # Define the derivatives\n",
    "    dphidr = v\n",
    "    dVdPhi = dVdphi(phi, temp, phiTest=h) \n",
    "    dvdr = - (alpha/r)*v + dVdPhi    # - (alpha/r)*v is the friction term, dVdphi(phi) the derivative of the potential (-)V(phi)\n",
    "    #print(\"r: \", r, \"dvdr\", dvdr, \"\\n\")\n",
    "    \n",
    "    # Set dy/dr = [dphi/dr, dv/dr]\n",
    "    dydr = np.array([dphidr, dvdr])\n",
    "    \n",
    "    return dydr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def findAction(phiB, dPhiB, rad_span, temperature):\n",
    "    potentialBounce = potential(phiB, temperature)\n",
    "    potentialFalseVacuum = potential(0, temperature)\n",
    "    integrand = rad_span**2*(0.5*dPhiB**2 + (potentialBounce - potentialFalseVacuum))\n",
    "    integral = np.trapz(integrand, rad_span)\n",
    "    S = integral*4*np.pi\n",
    "    action = S/temperature\n",
    "    return action"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def shootingAction(r, phiTrueVacuum, phiFalseVacuum, undershoot, tol, temp):\n",
    "    \"\"\"\n",
    "    Shooting method to find the bounce solution.\n",
    "\n",
    "    EOM for the bounce:\n",
    "    \n",
    "        dphi^2/dr^2 = - (alpha/r)*dphi/dr + dV/dphi\n",
    "    \n",
    "    Like a point particle moving in a potential -V(phi) subject to a friction term.\n",
    "    r acts as a time coordinate, and phi the spatial coordinate.\n",
    "\n",
    "    There are two BCs for the bounce:\n",
    "        1.) dphi/dr = 0 at r = 0 (no singularities in the origin, starting from rest)\n",
    "        2.) phi(r) = phi_F at r = infinity  (the particle come at rest in the false vacuum phi_F when r=inf)\n",
    "\n",
    "    We can turn this BVP to an IVP, we want to find the initial placement of the particle near the true vacuum phi_T that fulfills the BCs.\n",
    "    We get the ICs:\n",
    "        1.) dphi/dr = 0 at r = 0\n",
    "        2.) phi(r) = phi_B at r = 0\n",
    "    \n",
    "    Where phi_B is the solution that fulfills BC 2.). \n",
    "    Setting dphi/dr = 0 and then an initial placement somewhere close to phi_T we get three different cases:\n",
    "        a) The particle come at rest at phi_F when r = inf  (right solution, phi_B)\n",
    "        b) The particle roll past phi_F (overshooting)\n",
    "        c) The particle does not reach phi_F and experiences damped oscillations around the minimum (undershooting)\n",
    "\n",
    "    When we have overshooting the initial placement of the particle is too close to phi_T and for undershooting\n",
    "    it is too far from phi_T and needs to be closer. By trial and error, i.e iterate between over- and undershooting and \n",
    "    correct the intial placement until we find the right solution, case a), i.e the bounce solution phi_B.\n",
    "\n",
    "    @param r: the \"time\" coordinate\n",
    "           phiTrueVacuum: The value of phi at the true vacuum\n",
    "           phiFalseVacuum: The value of phi at the false vacuum\n",
    "           undershoot: sets the initial placement of the particle s.t we get an undershoot by phiTrueVacuum + undershoot.\n",
    "           tol: Set tolerance for which we accept our numerical solution\n",
    "    @return y_num: The numerical solution of the bounce\n",
    "\n",
    "    \"\"\"\n",
    "    \n",
    "    # Set tolerance for which we accept our numerical solution\n",
    "    # and a maximum of iteration to abrupt the while loop \n",
    "    #tol = 1e-3\n",
    "    max_iters = 100\n",
    "    radius = 0\n",
    "\n",
    "\n",
    "    # Set a lower and higher bound for our initial placement of the particle. \n",
    "    # Should be choosen s.t high gives an overshoot and low an undershoot.\n",
    "    high = phiTrueVacuum\n",
    "    low = phiTrueVacuum - undershoot\n",
    "    \n",
    "    # BC 1.), dphi/dr = 0 at r = 0\n",
    "    dphidr0 = 0\n",
    "\n",
    "    # Count of iterations\n",
    "    count = 0\n",
    "\n",
    "    # Parameter needed for solve_ivp, the first and last value of r\n",
    "    xspan = (r[0], r[-1])\n",
    "\n",
    "\n",
    "    while count <= max_iters:\n",
    "        count = count + 1\n",
    "\n",
    "        # Set the intial guess of the placement, phi0, as the mean between over- and undershoot              \n",
    "        phi0 = np.mean([low, high])\n",
    "\n",
    "        # Collect the two initial conditions\n",
    "        f0 = [phi0, dphidr0]\n",
    "\n",
    "        #print('phi0: ', phi0)\n",
    "        # Solve our system of ODEs given as an IVP, evaluated at every point in r \n",
    "        sol = solve_ivp(equationsBounce, xspan, f0, method='LSODA', args = (temp, phi), dense_output = True)\n",
    "        z = sol.sol(r)\n",
    "\n",
    "        # The numerical solution from the solver\n",
    "        y_num = z[0, :]\n",
    "        #print(y_num[-1])\n",
    "\n",
    "        # If the initial placement was right, i.e phi0 = phi_B we have found our solution and break\n",
    "        # the while loop. check if value of the last point in our numerical solution is within tolerance to phi_F.\n",
    "        if np.abs(y_num[-1] - phiFalseVacuum) <= tol:\n",
    "            # Find the radius by finding the first value of r when phiB equals 0       \n",
    "            index = 0\n",
    "            for i in y_num:\n",
    "                if np.abs(i - phiFalseVacuum) <= 1:\n",
    "                    break\n",
    "                else:\n",
    "                    index += 1\n",
    "\n",
    "            radius = r[index-1]         \n",
    "            break\n",
    "        \n",
    "        # If the solution is not at the false vacuum we have either an over- or undershoot and \n",
    "        # we need to adjust our bounds. Depending on if phi_F is either to the righ or the left \n",
    "        # of phi_T the conditions for over- and undershoot will look different.\n",
    "\n",
    "        # When phi_T is placed to the right of phi_F\n",
    "        if phiTrueVacuum > phiFalseVacuum:\n",
    "            # We get an overshoot if the last point of y_num is smaller than phi_F or if\n",
    "            # it goes to +/- inf, we get the message 'Required step size is less than spacing between numbers.'\n",
    "            # from solv_ivp if it has very high or low values since it stops working\n",
    "            if sol.message == 'Required step size is less than spacing between numbers.'\\\n",
    "                or y_num[-1] < phiFalseVacuum or y_num[-1] > phiTrueVacuum or np.isnan(y_num[-1]):\n",
    "                high = phi0\n",
    "                #print('Overshoot \\n')\n",
    "\n",
    "            else:\n",
    "                low = phi0\n",
    "                #print('Undershoot \\n')\n",
    "\n",
    "    if radius == 0:\n",
    "        radius = r[-1]\n",
    "\n",
    "    #print(y_num[-1])\n",
    "        \n",
    "    R = np.linspace(r[0], radius, 100)\n",
    "    bounce = sol.sol(R)\n",
    "\n",
    "    # Get phi_B and dphi_B/dr needed for the Euclidean action\n",
    "    dPhiB = bounce[1,:]\n",
    "    phiB = bounce[0,:]\n",
    "\n",
    "    return y_num, dPhiB, phiB, radius, R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "actions = []\n",
    "temperatures = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Action:  576.6905371433506\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-1.0, 200.0)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "T = TC-0.6\n",
    "\n",
    "phiMin, = fsolve(findPhiMin, phi[70])\n",
    "\n",
    "r1 = np.linspace(0.00001, 0.55, 100)\n",
    "phiB_numLong1, dPhiB_num, phiB_num, radius, R = shootingAction(r1, phiMin, 0, undershoot = 2, tol = 1e-1, temp = T)\n",
    "\n",
    "action = findAction(phiB_num, dPhiB_num, R, T)\n",
    "print(\"Action: \", action)\n",
    "\n",
    "actions.append(action)\n",
    "temperatures.append(T)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(r1, phiB_numLong1, label='T1')\n",
    "plt.xlabel('r')\n",
    "plt.ylabel('$\\phi_B$(r)')\n",
    "plt.ylim([-1, 200])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Action:  358.1315304630108\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-1.0, 200.0)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "T = TC-0.8\n",
    "\n",
    "phiMin, = fsolve(findPhiMin, phi[70])\n",
    "\n",
    "r2 = np.linspace(0.00001, 0.5, 100)\n",
    "phiB_numLong2, dPhiB_num, phiB_num, radius, R = shootingAction(r2, phiMin, 0, undershoot = 2, tol = 1e-1, temp = T)\n",
    "\n",
    "action = findAction(phiB_num, dPhiB_num, R, T)\n",
    "print(\"Action: \", action)\n",
    "\n",
    "actions.append(action)\n",
    "temperatures.append(T)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(r2, phiB_numLong2, label='T2')\n",
    "plt.xlabel('r')\n",
    "plt.ylabel('$\\phi_B$(r)')\n",
    "plt.ylim([-1, 200])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Action:  249.46958744123825\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-1.0, 200.0)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "T = TC-1.0\n",
    "\n",
    "phiMin, = fsolve(findPhiMin, phi[70])\n",
    "\n",
    "r3 = np.linspace(0.00001, 0.45, 100)\n",
    "phiB_numLong3, dPhiB_num, phiB_num, radius, R = shootingAction(r3, phiMin, 0, undershoot = 2, tol = 1e-1, temp = T)\n",
    "\n",
    "action = findAction(phiB_num, dPhiB_num, R, T)\n",
    "print(\"Action: \", action)\n",
    "\n",
    "actions.append(action)\n",
    "temperatures.append(T)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(r3, phiB_numLong3, label='T3')\n",
    "plt.xlabel('r')\n",
    "plt.ylabel('$\\phi_B$(r)')\n",
    "plt.ylim([-1, 200])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Action:  214.09472256120725\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-1.0, 200.0)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "T = TC-1.1\n",
    "\n",
    "phiMin, = fsolve(findPhiMin, phi[70])\n",
    "\n",
    "r4 = np.linspace(0.00001, 0.45, 100)\n",
    "phiB_numLong4, dPhiB_num, phiB_num, radius, R = shootingAction(r4, phiMin, 0, undershoot = 2, tol = 1e-1, temp = T)\n",
    "\n",
    "action = findAction(phiB_num, dPhiB_num, R, T)\n",
    "print(\"Action: \", action)\n",
    "\n",
    "actions.append(action)\n",
    "temperatures.append(T)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(r4, phiB_numLong4, label='T4')\n",
    "plt.xlabel('r')\n",
    "plt.ylabel('$\\phi_B$(r)')\n",
    "plt.ylim([-1, 200])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Action:  186.08870846859784\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-1.0, 200.0)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "T = TC-1.2\n",
    "\n",
    "phiMin, = fsolve(findPhiMin, phi[70])\n",
    "\n",
    "r5 = np.linspace(0.00001, 0.42, 100)\n",
    "phiB_numLong5, dPhiB_num, phiB_num, radius, R = shootingAction(r5, phiMin, 0, undershoot = 2, tol = 1e-1, temp = T)\n",
    "\n",
    "action = findAction(phiB_num, dPhiB_num, R, T)\n",
    "print(\"Action: \", action)\n",
    "\n",
    "actions.append(action)\n",
    "temperatures.append(T)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(r5, phiB_numLong5, label='T5')\n",
    "plt.xlabel('r')\n",
    "plt.ylabel('$\\phi_B$(r)')\n",
    "plt.ylim([-1, 200])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Action:  173.47636518828443\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-1.0, 200.0)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "T = TC-1.3\n",
    "\n",
    "phiMin, = fsolve(findPhiMin, phi[70])\n",
    "\n",
    "r6 = np.linspace(0.00001, 0.33, 100)\n",
    "phiB_numLong6, dPhiB_num, phiB_num, radius, R = shootingAction(r6, phiMin, 0, undershoot = 2, tol = 1e-1, temp = T)\n",
    "\n",
    "action = findAction(phiB_num, dPhiB_num, R, T)\n",
    "print(\"Action: \", action)\n",
    "\n",
    "actions.append(action)\n",
    "temperatures.append(T)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(r6, phiB_numLong6, label='T6')\n",
    "plt.xlabel('r')\n",
    "plt.ylabel('$\\phi_B$(r)')\n",
    "plt.ylim([-1, 200])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Action:  156.61148790097923\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-1.0, 200.0)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "T = TC-1.4\n",
    "\n",
    "phiMin, = fsolve(findPhiMin, phi[70])\n",
    "\n",
    "r7 = np.linspace(0.00001, 0.29, 100)\n",
    "phiB_numLong7, dPhiB_num, phiB_num, radius, R = shootingAction(r7, phiMin, 0, undershoot = 2, tol = 1e-1, temp = T)\n",
    "\n",
    "action = findAction(phiB_num, dPhiB_num, R, T)\n",
    "print(\"Action: \", action)\n",
    "\n",
    "actions.append(action)\n",
    "temperatures.append(T)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(r7, phiB_numLong7, label='T7')\n",
    "plt.xlabel('r')\n",
    "plt.ylabel('$\\phi_B$(r)')\n",
    "plt.ylim([-1, 200])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Action:  147.33429612025728\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-1.0, 200.0)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "T = TC-1.5\n",
    "\n",
    "phiMin, = fsolve(findPhiMin, phi[70])\n",
    "\n",
    "r8 = np.linspace(0.00001, 0.28, 100)\n",
    "phiB_numLong8, dPhiB_num, phiB_num, radius, R = shootingAction(r8, phiMin, 0, undershoot = 2, tol = 1e-1, temp = T)\n",
    "\n",
    "action = findAction(phiB_num, dPhiB_num, R, T)\n",
    "print(\"Action: \", action)\n",
    "\n",
    "actions.append(action)\n",
    "temperatures.append(T)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(r8, phiB_numLong8, label='T8')\n",
    "plt.xlabel('r')\n",
    "plt.ylabel('$\\phi_B$(r)')\n",
    "plt.ylim([-1, 200])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Action:  133.08738974620795\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-1.0, 200.0)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "T = TC-1.6\n",
    "\n",
    "phiMin, = fsolve(findPhiMin, phi[70])\n",
    "\n",
    "r9 = np.linspace(0.00001, 0.265, 100)\n",
    "phiB_numLong9, dPhiB_num, phiB_num, radius, R = shootingAction(r9, phiMin, 0, undershoot = 2, tol = 1e-1, temp = T)\n",
    "\n",
    "action = findAction(phiB_num, dPhiB_num, R, T)\n",
    "print(\"Action: \", action)\n",
    "\n",
    "actions.append(action)\n",
    "temperatures.append(T)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(r9, phiB_numLong9, label='T9')\n",
    "plt.xlabel('r')\n",
    "plt.ylabel('$\\phi_B$(r)')\n",
    "plt.ylim([-1, 200])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Action:  127.72319498980501\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-1.0, 200.0)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "T = TC-1.7\n",
    "\n",
    "phiMin, = fsolve(findPhiMin, phi[70])\n",
    "\n",
    "r10 = np.linspace(0.00001, 0.26, 100)\n",
    "phiB_numLong10, dPhiB_num, phiB_num, radius, R = shootingAction(r10, phiMin, 0, undershoot = 2, tol = 1e-1, temp = T)\n",
    "\n",
    "action = findAction(phiB_num, dPhiB_num, R, T)\n",
    "print(\"Action: \", action)\n",
    "\n",
    "actions.append(action)\n",
    "temperatures.append(T)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(r10, phiB_numLong10, label='T10')\n",
    "plt.xlabel('r')\n",
    "plt.ylabel('$\\phi_B$(r)')\n",
    "plt.ylim([-1, 200])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Action:  115.86467481690707\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-1.0, 200.0)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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bR/D83U1Yu/c0T3+chAcsWSYexLTVVUXKu7gOtTidns3sfx6gcpAP4//UwOxIIoCKQcRU43vU5/TFbF7/5wEqBfkS176m2ZFEVAwiZrJYLLzQqympGdk892kSVYN86d5Yy3WLuTTHIGIyu83K7AEtaVotmNH/t1PrKonpVAwibsDf2878+9sQ6vBmyPvbOHruktmRpBxTMYi4ifBAX95/8Cay8/J58P2tugBOTKNiEHEj9SoH8nZcaw6lZjJq8U5d4yCmcGkxJCYmEhcXB8CePXsYMGAAcXFxPPTQQ6SmXrnTVXx8PL179yYuLo64uDjS07VUsZQvHeuEEX9PU9bvP0P8qj1mx5FyyGVnJc2bN4+EhAT8/PwAeOGFF3j22Wdp1KgRS5YsYd68eUyaNInk5GTmz59PaGioq6KJuJ1+bSM5cDqD+RsOUqeSg7gOtcyOJOWIy/YYIiMjmT17dsHnM2fOpFGjRgDk5+fj4+OD0+nk8OHDTJkyhX79+vHRRx+5Kp6I25l0RyNuaxjO1L+n6N7R4lIuK4aYmBjs9n/voISHhwOwY8cOFi5cyAMPPMClS5cYNGgQL7/8MvPnz2fx4sXs3bvXVRFF3IrNauHVfi2oHebg0cU7dKaSuIypk8+rV6/mueee45133iE0NBQ/Pz8GDx6Mn58fAQEBtG/fXsUg5VqgrxfzBrfBMGDoh9vIzM4zO5KUA6YVw6effsrChQtZsGABNWrUAODQoUP079+f/Px8cnNz2bFjB02aNDEroohbqBXmYM6Aluw/lc7jyxJxOrXgnpQuU5bEyM/P54UXXqBq1aqMHj0agJtuuokxY8bQs2dP+vbti5eXFz179qRevXpmRBRxK53rVWLyHY2IX7WHN7/5iZHd6podSTyYxfCA9X579+7NypUrzY4hUqoMw2Dc0l0kJJ7ggwfb0qV+JbMjSRn3Rz87dYGbSBlhsVj4a+9mNKgcyJglOzUZLaVGxSBShvh723k7rjVOp8GwBdt1a1ApFSoGkTKmZkUHr/VrScrJizz3abLZccQDqRhEyqBuDcMZfWtdlm47yrJtR82OIx5GxSBSRo3rXp+OdSry7CdJpJy4aHYc8SAqBpEyyma18Fq/lgT7efHoou2ka5luKSEqBpEyrFKgD3MGtOLo+cs8tfIHPODsc3EDKgaRMq5tVCjje9Rn1e6T/N8WzTfIjVMxiHiAEV3r0LleGH/5ezJ7Tmq+QW6MikHEA1itFmbFtiDIz4uRi3dosT25ISoGEQ8RFuDDa/1acDA1k6kJur5Bik/FIOJBOtYJY3S3uizffoxPdx03O46UUSoGEQ8z5rZ6tK5ZgWc+TuLIWa2nJEWnYhDxMHabldf6tQALjFmyk9x8p9mRpIy57mLYtm0bo0ePpmPHjnTt2pVbb72Vxx9/nB07dpRmPhEphuoV/Jl+bzS7jl7g1a/2mx1HypjrulHPtGnTCAgIYPTo0dStWxer9Uqf7Nu3j4SEBBISEpg6dWpp5hSRIrqjWVVi29Rg7rqf6FKvEu1qVzQ7kpQR11UMjz76KBUrVuT7778vKAWABg0aMHHiRFJTU0stoIgU35S7GrPl0DkeW7qLz8d2Idjfy+xIUgZc16GkihWv/KYxe/bs330+LCys5BKJSIlx+Nh5NbYFp9OzmfyJlsyQ61Okez5bLBZGjhxJVFRUwZ7D+PHjSyWYiJSM5jVCeKxHfV7+ch/dGoTTp3V1syOJmytSMdx777039GaJiYm88sorLFiwgMOHD/PUU09hsVioV68ezz33HFarlTlz5rBu3TrsdjuTJ08mOjr6ht5TRGB41zp8s/8MUxOSaRcVSo1Qf7MjiRsrUjH06tWr2G80b948EhIS8PPzA+Cvf/0r48aNo127dkyZMoW1a9cSERHBli1bWL58OSdPnmT06NGsWLGi2O8pIlfYrBZm9m3O/7z6LY8t3cXSYR2wWS1mxxI3dV1zDFOmTGH//t8/5W3Pnj1MmTLlmt8jMjKy0BxFcnIybdu2BaBLly5s3LiR7du306lTJywWCxEREeTn53Pu3LnriSgi11C9gj/T7mnKtsPneeubn8yOI27suvYYxo8fz6uvvkpSUhJRUVGEhYVx8eJF9uzZQ3R0NOPGjbvm94iJieHYsWMFnxuGgcVy5TcWh8NBeno6GRkZhISEFHzNvx4PDQ0t2qhE5Hf1bBHBV3tOMWvNfjrXCyO6eojZkcQNXVcxhISEMHXqVDIyMkhMTOT8+fNUrFiRp59+Gn//4h2r/M/TXjMzMwkKCiIgIIDMzMxCjwcGBhbr+4vIb1ksFl64pxnbDp3nsaW7+Gx0Z/y8bWbHEjdTpCUxAgICqFKlChUqVKBDhw6FfrgXVePGjdm8eTMA69evp02bNrRq1YoNGzbgdDo5ceIETqdTewsiJSzY34tX7mvOT2cymf7FXrPjiBsq0uQzQHx8PF27dmXx4sXYbDbq1KnD2LFji/zGTz75JM8++ywzZ86kdu3axMTEYLPZaNOmDbGxsTidzuuauxCRoutUL4wHb67Fe98d4taG4XSpX8nsSOJGilwMderU4YEHHuDQoUNMnTqV559//rpfW716dZYtWwZAVFQUCxcu/M3XjB49mtGjRxc1logU0ZO3N+TbH1OZ+FEiX47rQoi/t9mRxE0U+VjQzp07ef755zly5Aj79u3TlZQiZZSvl41XY1twNiOHZz5JMjuOuJEi7THk5OSwaNEiLly4QFJSEl988QUnTpworWwiUsqaVgtmXPd6vPKP/fypyQnubh5hdiRxA9ddDB988AFz587Fx8cHh8PBwIEDizW3ICLuZXjXOqzde5pnPv6BtrVCqRLsa3YkMdk1DyXFx8fz8ccf8+GHH7J69WrWr1/PokWLOHDgAK+99porMopIKbLbrMzs24LcfIOJHyXq8LBcuxjat2/PkSNHOH/+PP369aNXr1787W9/IzIyklWrVpGWluaKnCJSiqLCHEz+cyO+/TGVhd8fNjuOmOyah5K6d+9O9+7dSUxMZNKkSVSqVIl9+/axd+9e0tLSuP/++8nIyOCrr75yRV4RKSWD2kWyJuUUL6zeQ6d6lYgKc5gdSUxy3WclTZkyhYkTJzJ9+nRSUlL48ccfqV+/Pp988gmrV68uzYwi4gIWi4W/3RuNj93G+GW7yNO9osut6y6GWrVqsWzZMmJiYsjOzqZBgwbMmTMHAG9vnf8s4gmqBPsy7Z6m7DxygbfX/2x2HDFJkU5X9fb25pZbbuGWW24ppTgiYra7m0fwj+RfmLVmP13rV6JptWCzI4mLFX+xIxHxWNN6NiXU4c34ZbvIys03O464mIpBRH6jgsObv/WJZv+pDGau+f17sYjnUjGIyO+6pUE4A9tFMu/bn/n+57NmxxEXUjGIyB+afEcjIkP9mbA8kfSsXLPjiIuoGETkDzl87Mzs25wTFy4z7bMUs+OIi6gYROSqWtcMZXjXOizbdox/JP9idhxxARWDiFzTuO71aVw1iEkrfyA1I9vsOFLKVAwick3ediuzYluQnp3HUyt+0EJ7Hk7FICLXpUGVQJ6IacBXe06xfNsxs+NIKVIxiMh1G3JzFB1qV+Qvf0/myNlLZseRUmJqMaxcuZK4uDji4uLo27cvzZo1Y82aNXTv3r3g8S1btpgZUUT+g9Vq4ZW+zbFaLTymhfY8lsVwk4OFf/nLX2jYsCEnTpygcePGxMTEXPdre/fuzcqVK0sxnYj8p092Hmfc0l1M+FN9Rt1az+w4Ukx/9LPTLQ4l/fDDDxw4cIDY2FiSk5NZsWIFAwYM4KWXXiIvL8/seCLyX3q2iOCu5hG8+tWP7D52wew4UsLcohjefvttRo4cCcDNN9/Ms88+y6JFi7h06RJLliwxOZ2I/DeLxUJ8z6ZUCvRh3NJdXM7RQnuexPRiuHjxIgcPHqR9+/YA3HvvvdSoUQOLxcJtt91GSoquthRxR8H+Xsy4rzkHUzOJX6V/p57E9GLYunUrHTp0AMAwDO6++25++eXK1ZWbNm2iSZMmZsYTkavoWDeMRzrXZtHmI6xJOWV2HCkhphfDwYMHqV69OvDr7ml8PKNGjWLQoEFcvnyZvn37mpxQRK5m/J+uXBX95IrdnE7PMjuOlAC3OSvpRuisJBFzHTidzp9f30C72hV5/4GbsFotZkeS6+DWZyWJSNlWNzyQZ+5szPr9Z3j3u4Nmx5EbpGIQkRIxqF0kPRpXZvoXe0k6nmZ2HLkBKgYRKREWi4Xp90YT6vBmzJKdXMrRNUhllYpBREpMqMObWX1bcDA1k+f/rlNYyyoVg4iUqI51wxjetQ5Lth7l74knzI4jxaBiEJESN75HfVpGhjB55Q9ahbUMUjGISInzsll5vV9LLBYY/X87yMnTKqxliYpBREpFjVB/pt8bTeKxNF7+cq/ZcaQIVAwiUmr+p1lVBrWPZN63B1m7R0tmlBUqBhEpVc/8uTGNqwYxflkix85rvqEsUDGISKny9bIxd2Ar8p0Goxbv1HxDGaBiEJFSVyvMwd/6RLPr6AWmf6H5BnenYhARl7ijWVUe6FiL/91wkC+STpodR65CxSAiLjPpjoY0rxHChOW7+flMhtlx5A+oGETEZXzsV+YbvGwWRizcofWU3JSKQURcqlqIH6/1a8n+0+k8/XESHnBLGI+jYhARl+tSvxLju9fn453H+XDTYbPjyH9RMYiIKUZ2q0v3RuFM+yyFzT+fNTuO/AcVg4iYwmq1MDO2BZGh/oxcvIOTaZfNjiS/spsdoFevXgQEBABQvXp1YmNjeeGFF7DZbHTq1IlRo0aZnFBESkuQrxfvDG7NPW9sZPiC7Swd1gFfL5vZsco9U4shOzsbwzBYsGBBwWM9e/Zk9uzZ1KhRg0ceeYSUlBQaN25sYkoRKU11wwOZ0bc5wxZs5+mPk3jlvmgsFovZsco1Uw8l7d27l8uXLzNkyBAGDx7M1q1bycnJITIyEovFQqdOndi4caOZEUXEBWKaVGFc93qs2HGM+d8eNDtOuWfqHoOvry8PPfQQ9913H4cOHWLo0KEEBQUVPO9wODh69KiJCUXEVcbcWo/9p9L56+d7qFs5gG4Nws2OVG6ZuscQFRXF3XffjcViISoqisDAQC5cuFDwfGZmZqGiEBHPZbVaeOW+5jSsEsSYxTs5cDrd7EjllqnF8NFHH/HSSy8BcOrUKS5fvoy/vz9HjhzBMAw2bNhAmzZtzIwoIi7k721n/v1t8PGyMeT9bZzNyDY7Urlk6qGkPn36MGnSJPr374/FYuHFF1/EarUyYcIE8vPz6dSpE82bNzczooi4WESIH/MGt6bfO9/zyILtLHq4nc5UcjFTi8Hb25sZM2b85vFly5aZkEZE3EXLyArMim3Bo4t28MRHu3mtXwudqeRCusBNRNzSHc2q8sTtDUhIPMGsNfvNjlOumH6Bm4jIHxnRtQ6HUy/x+j8PEBHiR7+2kWZHKhdUDCLitiwWC/G9mvLLxSye/iSJykG+dGuo01hLmw4liYhb87JZmTuwFY2qBvLooh0kHr1gdiSPp2IQEbfn8LHz7gM3ERbozZD3t+rub6VMxSAiZUJ4oC8fDmkHQNz/buGXtCyTE3kuFYOIlBlRYQ4+GNKWtMu5DH53Mxcu5ZgdySOpGESkTGlaLZh3BrfmUOolHnhvKxnZum90SVMxiEiZ07FOGLMHtOSH42kM/WAbWbn5ZkfyKCoGESmTYppUYcZ9zfn+4FlGLNxOTp7T7EgeQ8UgImXWPS2r8WKvZny97wxjl+wkN1/lUBJUDCJSpvVvG8mUOxvzedIvjFu6izyVww3Tlc8iUuYN6RRFvtPghdV7sFoszOrbHLtNv/cWl4pBRDzC0C61yTcMXvp8L1YLzLhP5VBcKgYR8RjDu9bBaRj87Yt95OUbvNqvBV4qhyJTMYiIR3n0lrp426zEr9pDTr6TOQNa4mPXjX6KQlUqIh7n4c61eb5nE9aknOKRD7dzOUfXORSFikFEPNLgDrV4qXcz1v94hvvf3cLFrFyzI5UZKgYR8Vj92kYyu39Ldh49T/93vudsRrbZkcoEFYOIeLQ7oyOYN7gNP53J4L63N3Hs/CWzI7k9U4shNzeXiRMnMmDAAPr06cPatWtJSUmhc+fOxMXFERcXx+rVq82MKCIe4JYG4Sx4qB2p6dn0nruRlBMXzY7k1kw9KykhIYGQkBBefvllLly4wD333MPIkSN58MEHGTJkiJnRRMTD3FQrlOXDO3L/u1uIfXsTbw9uTcc6YWbHckum7jHcfvvtjB07FgDDMLDZbCQlJbFu3ToGDhzI5MmTycjQnZpEpGQ0qBLIykc7UiXYlwfe3conO4+bHcktmVoMDoeDgIAAMjIyGDNmDOPGjSM6OponnniCRYsWUaNGDd544w0zI4qIh4kI8eOj4R1pVTOEcUt38fraHzEMw+xYbsX0yeeTJ08yePBgevbsyV133UWPHj1o2rQpAD169CAlJcXkhCLiaYL9vfhwSDt6t6rGzDX7mbB8t5bt/g+mFkNqaipDhgxh4sSJ9OnTB4CHHnqI3bt3A7Bp0yaaNGliZkQR8VDedisz7mvOY93rs2LHMQbO/55Unc4KmDz5/NZbb3Hx4kXmzp3L3LlzAXjqqad48cUX8fLyIiwsjGnTppkZUUQ8mMViYWz3etSu5GDC8kR6zvmO+fe3oVHVILOjmcpieMDBtd69e7Ny5UqzY4hIGbb72AWGfriN9Kw8ZvZtzu1Nq5odqdT90c9O0+cYRETcQXT1EBJGdaJe5UCGL9zBy1/uJd9Z5n9vLhYVg4jIryoH+bJsWHti29Tgja9/Ysj7W7lwKcfsWC6nYhAR+Q8+dhsv3duMF3o1ZeNPqdw5ewO7j10wO5ZLqRhERP6LxWJhYLuaLBvWAafToM+bm1i0+XC5ud5BxSAi8gdaRlZg1ZjOdKhTkac/TmLskl2kl4Plu1UMIiJXUcHhzXsP3MTEmAas+uEkd87ewA/H0syOVapUDCIi12C1WhjZrS5LHmlPTp6T3m9+x/xvf8bpoWctqRhERK7TTbVCWT2mM7c0CCd+1R7uf28Lpy9mmR2rxKkYRESKoILDm3fiWvNCr6ZsPXSOmFfX82XyL2bHKlEqBhGRIvrXWUufje5MRIgfwxZsZ8LyRI+ZmFYxiIgUU93wAD5+9GZGdavLyh3HuP3Vb9n4U6rZsW6YikFE5AZ4261MiGnARyM64m23MmDeZp79JInM7DyzoxWbikFEpAS0iqzA6jGdGXJzFAs3Hybm1fVsPFA29x5UDCIiJcTP28aUuxqzbFgH7FYLA+Zv5smPdpN2uWzNPagYRERK2E21QvliXBeGda3NRzuO0X3mN3yRdLLMLKmhYhARKQW+XjYm/U8jPh15M5UCfBi+cAdDP9zOiQuXzY52TSoGEZFS1LRaMAmjbmbyHQ357kAqPWZ+w/9uOEhevvveY1rFICJSyuw2K490qcM/HutC26hQpn2Wwt1zvmPHkfNmR/tdKgYRERepEerPuw/cxFuDWnH+Ug69525k0srdnMt0r5sBuWUxOJ1OpkyZQmxsLHFxcRw+fNjsSCIiJcJisXB706p8Nb4rQztHsXzbMW6dsY6F3x92m1uJumUxfPXVV+Tk5LB06VIef/xxXnrpJbMjiYiUKIePnaf/3JjPx3amUZUgnvkkibvnbGDboXNmR3PPYti+fTudO3cGoEWLFiQlJZmcSESkdNSrHMjioe2Y3b8l5zJz6PPWJsYu2cnJNPPOXnLLYsjIyCAgIKDgc5vNRl5e2b28XETkaiwWC3c1j2Dt410Zc2tdPk/6hVtf+YbX1/7I5Zx8l+exu/wdr0NAQACZmZkFnzudTuz2P456/Phxevfu7YpoIiKlrumvH9clw7o3Su99jh8//ruPu2UxtGrViq+//po77riDXbt2Ub9+/at+/ebNm12UTETE81kMN7xG2+l0MnXqVPbv349hGLz44ovUqVPH7FgiIuWCWxaDiIiYxy0nn0VExDwqBhERKUTFICIihbjlWUkl5V+T2Pv27cPb25v4+Hhq1qxZ8PyyZctYsmQJdrudESNG0K1bN86dO8eECRPIysoiPDycv/71r/j5+Zk4iqIpzpgvXLhATExMwdlf3bt35/777zdrCEV2rTEDnDt3jv79+5OQkICPjw9ZWVlMnDiRs2fP4nA4mD59OqGhoSaNoGiKM17DMOjSpQu1atUCrlw4+vjjj5uQvniuNeb333+fVatWAdC1a1dGjRpVprcxFG/MJbadDQ/25ZdfGk8++aRhGIaxc+dOY/jw4QXPnT592rjzzjuN7Oxs4+LFiwV/nzZtmrFixQrDMAzj7bffNt577z0zohdbccb83XffGc8//7xZkW/Y1cZsGIaxfv16o2fPnkbLli2NrKwswzAM49133zVef/11wzAM47PPPjOmTZvm2tA3oDjjPXTokDFs2DCXZy0pVxvzkSNHjF69ehl5eXmG0+k0YmNjjT179pTpbWwYxRtzSW1njz6UdLWlNXbv3k3Lli3x9vYmMDCQyMhI9u7dW+g1Xbp0YePGjaZkL67ijDkpKYnk5GQGDRrEmDFjOH36tFnxi+VaS6hYrVbee+89QkJCfvc1Xbp0YdOmTS7Le6OKM97k5GROnTpFXFwcQ4cO5eeff3Zl5Bt2tTFXqVKF+fPnY7PZsFgs5OXl4ePjU6a3MRRvzCW1nT26GK62tEZGRgaBgYEFzzkcDjIyMgo97nA4SE9Pd23oG1ScMdeuXZsxY8awcOFCunfvTnx8vMtz34hrLaFy8803U6FChd+8pqxu5+KMt1KlSjzyyCMsWLCAYcOGMXHiRJflLQlXG7OXlxehoaEYhsH06dNp3LgxUVFRZXobQ/HGXFLb2aPnGK62tMZ/P5eZmUlgYGDB476+vmRmZhIUFOTy3DeiOGOOjo4umEfp0aMHr7/+umtD36CiLqHy368pa9u5OONt2rQpNpsNgDZt2nD69GkMw8BisZRq1pJyrTFnZ2czefJkHA4Hzz333G9eU9a2MRRvzCW1nT16j6FVq1asX78e4DdLa0RHR7N9+3ays7NJT0/np59+on79+rRq1YpvvvkGgPXr19O6dWtTshdXccb8zDPP8OWXXwKwadMmmjRpYkr24rramK/2mrK6nYsz3jlz5vDBBx8AsHfvXqpWrVpmSgGuPmbDMHj00Udp0KABzz//fMEPxrK8jaF4Yy6p7ezRVz7/3tIa69evJzIykttuu41ly5axdOlSDMNg2LBhxMTEkJqaypNPPklmZiYVKlRgxowZ+Pv7mz2U61acMR89epTJkycD4OfnR3x8POHh4SaP5Ppda8z/cuutt/L555/j4+PD5cuXefLJJzlz5gxeXl7MmDGDSpUqmTiK61ec8aalpTFx4kQuXbqEzWZjypQpZWqZmauN2el0Mn78eFq0aFHw9ePHj6dhw4ZldhtD8cZcu3btEtnOHl0MIiJSdB59KElERIpOxSAiIoWoGEREpBAVg4iIFKJiEBGRQlQMIiJSiIpBREQKUTGIlJKVK1cycOBA+vfvX+YWcJPyzaPXShIxW1BQEG+++abZMUSKRHsMIqUoKirK7AgiRaZiEClFVqv+iUnZo/9rRUSkEC2iJyIihWiPQUREClExiIhIISoGEREpRMUgIiKFqBhERKQQFYOIiBSiYhARkUJUDCIiUsj/A+RrfhReWzvOAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "T = TC-1.8\n",
    "\n",
    "phiMin, = fsolve(findPhiMin, phi[70])\n",
    "\n",
    "r11 = np.linspace(0.00001, 0.25, 100)\n",
    "phiB_numLong11, dPhiB_num, phiB_num, radius, R = shootingAction(r11, phiMin, 0, undershoot = 2, tol = 1e-1, temp = T)\n",
    "\n",
    "action = findAction(phiB_num, dPhiB_num, R, T)\n",
    "print(\"Action: \", action)\n",
    "\n",
    "actions.append(action)\n",
    "temperatures.append(T)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(r11, phiB_numLong11, label='T11')\n",
    "plt.xlabel('r')\n",
    "plt.ylabel('$\\phi_B$(r)')\n",
    "plt.ylim([-1, 200])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Action:  115.21765625306969\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-1.0, 200.0)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "T = TC-1.9\n",
    "\n",
    "phiMin, = fsolve(findPhiMin, phi[70])\n",
    "\n",
    "r12 = np.linspace(0.00001, 0.25, 100)\n",
    "phiB_numLong12, dPhiB_num, phiB_num, radius, R = shootingAction(r12, phiMin, 0, undershoot = 2, tol = 1e-1, temp = T)\n",
    "\n",
    "action = findAction(phiB_num, dPhiB_num, R, T)\n",
    "print(\"Action: \", action)\n",
    "\n",
    "actions.append(action)\n",
    "temperatures.append(T)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(r12, phiB_numLong12, label='T12')\n",
    "plt.xlabel('r')\n",
    "plt.ylabel('$\\phi_B$(r)')\n",
    "plt.ylim([-1, 200])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TC =  125.21\n",
      "TN =  123.66\n",
      "beta/H:  19718.0\n",
      "Latent heat:  0.029\n"
     ]
    },
    {
     "data": {
      "image/png": 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NDSU8PJxdu3Y5KoqIyJ2J+h6OrINH3oEiAWancQiHlEBmZiYjRozA29sbgI8++ogBAwYwe/ZsDMNg1apVREVFsXXrVubPn8/48eN57733HBFFROTOpCfDimG2GcOCXzA7jcM4pATGjRtHeHg4pUuXBiAqKoqGDRsC0Lx5czZu3EhkZCQhISFYLBYCAwPJzs7m7NmzjogjInL71oyF5JPQ/jNwczc7jcPYvQQiIiIICAjgoYceyrnNMAwsl4+o+/j4kJycTEpKCr6+vjn3uXK7iIjpTu6BzZOhwXNQLtjsNA5l94vFFi5ciMViYdOmTezbt48hQ4bk+oafmpqKv78/vr6+pKam5rrdz8/P3nFERG6P1Qo/DrKND/ToSLPTOJzdtwRmzZrFzJkzmTFjBrVq1WLcuHE0b96cLVu2ALB27VqCg4OpX78+69evx2q1Eh8fj9VqJSCgYB54EREn8vsMOLYFWr1XYA8G/1WeDBsxZMgQhg8fzvjx4wkKCqJt27a4u7sTHBxMWFgYVquVESOce3YeESkAkk/CyuFQMQQe7G52mjxhMQzDMDvE7ejUqRMRERFmxxCRgui7nnBgOfTbCCWrmp0mT+hiMRERgP0/wt4foMVbLlMAoBIQEbFNGP/jYCh9HzR73ew0eUpDSYuI/PwupJyEsJng7ml2mjylLQERcW3Rq2D7t9C0P5RrYHaaPKcSEBHXlXYeFr8GJWvAwwVzgLib0e4gEXFdP78LyfHQ+xfw9DY7jSm0JSAirunQL7B9OjR9zSV3A12hEhAR15OaCD+8DKVqwcNDzU5jKu0OEhHXYhiw9HW4dA66L3TZ3UBXaEtARFzLjtmwbwm0fBfuecDsNKZTCYiIy9i9ZycZSweTfE8jaPKq2XHyBZWAiLiEyD8SyJ7/AmlZ8NTx7kQeu2B2pHxBJSAiLsHy62jqWaJ5O7MPsVkl2Hw40exI+cINS2Dv3r15lUNExHGif6H+sW+Za23FCqMxnh5uNA4qYXaqfOGGJTB27Ni8yiEi4hjJJyHiJShdm+rPTWJQmxrM6tOYBhWLm50sX9ApoiJScGVnwcI+kJEKod9Qv3RZ6lcxO1T+csMS2L59OyEhIddctn79eocEEhGxm18/gCProON/oXRNs9PkSzcsgQcffJAZM2bkVRYREfvZvww2TIAGvaBeV7PT5Fs6O0hECp6zh+H7f0LZevDYOLPT5Gs3LIGXXnqJ7OzsvMoiInL3MlJhXg+wWKDLdJcfFuJmbrg7KDo6mnnz5lG4cGGaNWtGixYtKFasWB5FExG5TYYBi16GhL3QbQEUr2h2onzPYhiGcbM7paSksG7dOtatW8fx48dp1qwZffv2zYt8V+nUqRMRERGmvLaI5HNrP7EdDG79ATR7zew0TuGGu4OioqLo2LEjXl5euLu7s3r1ak6ePJlX2UREbt2B5fDraHigi22qSLklNyyBf/3rX4wdOxZPT08mTJjAV199xcKFC/n111/zKp+IyM2d3AMLe0PZOvDkf2zHA+SW3PCYgNVqpWbNmpw6dYpLly5x3333AeDmppOKRCSfSD4Fs8PAyw+6zgXPwmYncio3LAEPD9videvW0aRJEwAyMzNJTU11fDIRkZvJuAhzu8Kls/D8T+AfaHYip3PDEmjSpAnh4eGcPHmSyZMnc/ToUd5//33atWuXV/lERK7NaoXvX4Lj2yF8FgTWMzuRU7phCfTt25dHH30UX19fypQpw9GjRwkLC6N169Z5lU9E5GqGASuGwr7F0GYM1HzC7ERO66YDyFWp8udoSxUqVKBChQoODSQiclMbJ8KW/0LjV6CpZgi7GzrCKyLOZdd8WDkc7nsa2ow2O43TUwmIiPM4+DMs+idUDLGNDKozFe+afoIi4hxiN8J3PaDMfdB1tsYEshOVgIjkfyd22q4FKFoeukeAd1GzExUYKgERyd8S9sGMp8HLH3p8Dz4lzU5UoDhkesns7Gzeffdd/vjjDywWC++99x5eXl68/fbbWCwWqlWrxsiRI3Fzc2PSpEmsWbMGDw8Phg0bRp06dRwRSUSc0ZlD8O2T4OYJPX+AYuXNTlTgOKQEVq9eDcDcuXPZsmULn332GYZhMGDAABo1asSIESNYtWoVgYGBbN26lfnz53PixAn69+/PwoULHRFJRJxNYgx82wEw4LnFULKq2YkKJIeUQKtWrXj44YcBiI+Px9/fn40bN9KwYUMAmjdvzoYNG6hcuTIhISFYLBYCAwPJzs7m7NmzBAQEOCKWiDiLxBjbFkBWOvT6EUrVMDtRgeWwYwIeHh4MGTKEDz74gA4dOmAYBpbLI/v5+PiQnJxMSkoKvr6+OY+5cruIuLDTB2HaE5B1ybYFUKa22YkKNIceGB43bhwrVqxg+PDhpKen59yempqKv78/vr6+uQajS01Nxc/Pz5GRRCQ/S9hnKwBrFjy3FO55wOxEBZ5DSmDRokVMmTIFgMKFC2OxWLj//vvZsmULAGvXriU4OJj69euzfv16rFYr8fHxWK1W7QoScVXxO2wFYHGDXsu0BZBHHHJMoE2bNgwdOpRu3bqRlZXFsGHDqFKlCsOHD2f8+PEEBQXRtm1b3N3dCQ4OJiwsDKvVyogRIxwRR0TyuyMbYE647fz/nj9AiSo3f4zYxS3NMZyfaI5hkQLm4Ar4ricUqwA9FkHRe81O5FJ0sZiImGfHHJj7LJSqaZsURgWQ51QCIpL3DAPWfXp5MLhm8NwSXQlsEoccExARuS5rNvw0BH77Eh7oDE99AR6FzE7lslQCIpJ30lNgYW84uByavgat3tNw0CZTCYhI3jh/HOaEwam98MSn8I8+ZicSVAIikheOb7cdAE5PgW7fQdVWZieSy7QdJiKOtWs+fPO4bSTQ3j+rAPIZbQmIiGNYs2HV+7Bhgm06yC7f6gygfEglICL2d/EsLOwDMasg+AV4/F/g7ml2KrkGlYCI2Ff8DttcwMknof0ECH7e7ERyAyoBEbEPw4DfZ8KywVCkBDy/HMo1MDuV3IRKQETuXkYq/PgG7JwDlVtA6P9p/7+TUAmIyN1J2A/zn4PTB6DF29DiLXBzNzuV3CKVgIjcGcOA7d/CT29DIR/oEQFVWpqdSm6TSkBEbt+lJFjyOuxdBEEPw9NTwO8ek0PJnVAJiMhtObDlJwJ/HYBvxmksj46EZgM0/o8T07+ciNyarAxOLHybasu6knjJICxrFJEVnlcBODltCYjIzZ3aC9/3pezJ3cy1PsL7mT1It3iz+XAiDSoWNzud3AWVgIhcnzUbNk6E1WPAy5/ollMYtbIomRYrnh5uNA4qYXZCuUsqARG5tjPR8MPLcGwL1GwP7SdQ1bcUsyqeY/PhRBoHldBWQAGgEhCR3KzZsHky/PoBeHjZzvypEwYWCwANKhbXyr8AUQmIyJ8S9sPi/hC3Fao/Dh0m6NTPAk4lICKQnQnrJ8Daf9ku/Hp6KtTpkvPtXwoulYCIq4uLhCWvwak9cF8n27DPvqXMTiV5RCUg4qrSk+HXMbDlv+BXFsJnQ80nzE4leUwlIOKK9v8Iy96CC8dtE74/OgK8/c1OJSZQCYi4kvNxtpX/gR+hdG3o/A2Ub2h2KjGRSkDEFWRn2nb7rP4IDCu0eg+avKIpH0UlIFLgHd0CSwdCQhRUawvt/gXFK5mdSvIJlYBIQZV6Bn4ZaZvy0f9eCJtpu/JXp33KX6gERAqYyD/OkLzxa0JiP8cjKxWavQ7N3wIvX7OjST6kEhApQPZtW02hJYN42HKYLUZtfDv9m/vq6sCvXJ9KQKQgSE2EVe9Rc/t0EijKaxmv8KPRlEFnA7jP7GySr6kERJxZdhZs+z9YPRrSU0i4rzftdjUlyfDWUM9yS1QCIs7qj7WwfKhtuIfKLeDxf1GmdE2mNtRQz3Lr7F4CmZmZDBs2jOPHj5ORkUG/fv2oWrUqb7/9NhaLhWrVqjFy5Ejc3NyYNGkSa9aswcPDg2HDhlGnTh17xxEpeBJjYOUI2L8UilaALtOh1pMa6lnuiN1LYPHixRQrVoyPP/6YpKQkOnbsSM2aNRkwYACNGjVixIgRrFq1isDAQLZu3cr8+fM5ceIE/fv3Z+HChfaOI1JwpCbC2o/ht69s4/w/OgIavwKe3mYnEydm9xJ47LHHaNu2LQCGYeDu7k5UVBQNG9rOUGjevDkbNmygcuXKhISEYLFYCAwMJDs7m7NnzxIQEGDvSCLOLSMVNn8B6/8NmanwYHd45F3wK2N2MikA3Oz9hD4+Pvj6+pKSksJrr73GgAEDMAwDy+VNVR8fH5KTk0lJScHX1zfX45KTk+0dR8R5ZVy0ze87oQ78OhqCWsDLm+HJiSoAsRu7lwDAiRMn6NmzJ0899RQdOnTAze3Pl0lNTcXf3x9fX19SU1Nz3e7n5+eIOCLOJe0CbPg3/Lsu/Pwu3PMA9F4J4bOgVA2z00kBY/cSOHPmDC+88AJvvvkmoaGhANSuXZstW7YAsHbtWoKDg6lfvz7r16/HarUSHx+P1WrVriBxbRfiYeVI+Ow+24Hf0rXg+eXQc5FG+hSHsfsxgf/+979cuHCBL774gi+++AKAd955h9GjRzN+/HiCgoJo27Yt7u7uBAcHExYWhtVqZcSIEfaOIpJvRcZePo2zcnEaZO+E376GAz8BBtTuCM1eg8AHzY4pLsBiGIZhdojb0alTJyIiIsyOIXLHImPPMeqr+TxurONJ902Us5yGIiVsB3wbPA8Blc2OKC5EF4uJ5IWsDDi2GQ6uoPLOpSxxP0KW4cYG4wH21nqdNqF9bad9iuQxlYCII6SnwIkdELsJYtfDsa2QeRHcC+FRphHvpzzC0syGXPAozqwmjVUAYhqVgMjdyrwEp6JsK/34HRD/OyTstc3gBVDmftuunsotIOhh/L18eSL2HCU0tIPkAyoBkduRngwndtlW9Cd2wsldcObgnyv8wsUhsD7UfALuDYZywVDk6rPeNLSD5BcqAZHriDxylv1RkTQrFEOli7vh2G+2FT6Xz6XwC4SydWzj9pSta/tVtJxm7hKnohIQ+auU0xD9C4m7f6Z89GoaWM4BkOVVDI8KjeD+Z2ynbgbWA9/S5mYVsQOVgEjCftuInAeXQ9w2wKCwZ3FWWWuywXofkUYNOjZ/hFdaVjM7qYjdqQTE9RiGbQz+qEWwb/HlXTzY9uU/Mgyqt2Vfejne/HormVarbXKWKiVNjSziKCoBcQ05K/7vbSv/szFgcYdKzaBhX6jZHvzL5ty9ATCrT2NNziIFnkpACq6/fuPfuwgSo8HiBpWb24ZlqNkefK7/DV9n8IgrUAlIwZKdBXG/wYEfYd8SOHfEtuKvFAJNXoGaHcC3lNkpRfINlYA4rSuDsD1UJpM6mbsgeiVE/wKXzoGbJwQ9DCGDoEY7rfhFrkMlIM7Fmg2nD3Bk1zqi163gMfZSxe2EbVmRklD9MajeFqq0BO+i5mYVcQIqAcmfrNmQFAtnoiHxkG0YhlN74fR+yLxIJSDAUoRt1urMy2pJlYbtCGvfDtwcMk+SSIGlEhDzXFnRnz0MZ/+AxBjbn8/9YduXn53x5319SkHp2lD/OQisxx5LVTrPP0VGFnh6uDGrbmMVgMgdUAmIQ0XGnmNzzGlalEzhfo9jtm/zCXvhzCHbaZp/XdF7FoGAINsUijUehxJVoUQ1KFntqrN47gdmFj2nUzhF7pJKQOwvIxWObubE7tWk7VhDD2Lwt1y0LbO42Vb0JWtA9TaXV/RVbbf5lrmtcXd0CqfI3VMJyN3LzoLjkRCzCg6vsf3ZmkUZ3DhnlGeptTG7jCrUb9SCLo+3As/CZicWkctUAnJnkk/aTsc89DPErIH087Zv+YEPQtP+UCmEndSk67e7ycy2Db3QuW5jFYBIPuNSJfDwww9fdVuXLl14+eWXuXjxIu3atbtqea9evejVqxdnzpwhNDT0quX9+vUjLCyMY8eO0aNHj6uWv/HGG3To0IEDBw7w0ksvXbX83XffpVWrVuzYsYMBAwZctfzDDz+kadOmbNy4kWHDhl21fMKECdSrV49ffvmF0aNHX7V8ypQp1KhRgyVLlvDpp59etXzGjBmUL1+eefPmMXny5KuWL1iwgJIlS/LtN//Hlu8n0zjgPI1KXKCG3yUArL734Fb7SVbEZDNp2W6Ss6zAmsu/YNa337P5cCKHfpnNG8+Ny/XchQsX5qeffgLggw8+YNWqVbmWlyhRgoULFwIwdOhQNm3alGt5uXLlmDlzJgADBgxgx44duZZXr16dqVOnAtC3b18OHjyYa3m9evWYMGECAN27dycuLi7X8iZNmvDRRx8B8Mwzz5CYmJhr+aOPPsrw4cMBePzxx7l06VKu5e3bt2fw4MGA/u/dzf+9adOmMW3atKuWL1u2jCJFivDFF1/w3XffXbV8zZo1AHzyyScsXbo01zJn/L935f3Ym0uVgNyee7zT8YqaB6e2En7sZ56rf5FsA/ac92Hq4bJsSfRn4nerKeLjQ8wXX5Ccte+q57iy3/6TyCLsyPu3ICI3YTEMwzA7xO3o1KkTERERZscoMK5cddu4UjEaFEmA49ts8+IeWQ/nj9ru5Bdou/iqakvb74V1MFakoNCWgKvJSIXzx+H8UY4d3En05g00JI6aliNgSbfdp3CAbXTNpq/aBlsrVVOzZYkUUCoBJ5Dzbf3v58NnZcCls3DxrO33S0mQlmT7/dK5y7/OQuoZSEmA1ATbbZeVB9pYfIk2AllobUHZ+0Jo/ejl8/N14ZWIS1AJ5GdpF9i3ZxvfLV5JWespjq4+TbXATPyzzkLKSUg7f/3HWtxsu20KF7ddbVuqum0kzaL3QtHyULQcOy+VImzWITKzDNtVt00aQynt6hFxJSqB/CIlAY5vhxM7IP53OLkHLsRRCxjnBlaLhVMUJ/ViefzvrWHbTeNbGooE2HbfFAkA72JQuJjtdy//m36brwvM6lNSV92KuDCVgBmsVji9D45ugqNbIG6rbawcACxQsjpUbAKlahJNefqvTOFIVgkMDy9mPdOYsnZcWeuqWxHXphLIC1kZcGInxG6A2I1wbPOfu3J874Hy/4Dg3lAuGO6pA16+OQ+tCoyuqDFyRMQxVAJ2cNWB27TztqETYjfZvu3HbYOsyxcSlagGtZ+CCk1t3/aLVbzpmTf6ti4ijuIyJRB55CxbY07RsOo9dl2hbj98ko++WUBNawwx7keoHRBH4aRDgGE7OHvPA9DgOajYFCo0se3HFxHJJ1yiBCJjz7Hz/16lj2U5+9dWJKF2c0pXbwgBlaF4JdsumesdRDUMyLwIqach6RicP2Yb+/7MAUjYT93EaBa4Z4M7JBk+JFjqUvHhUNsunnL/AC+/PH2vIiK3wyVKYPPhRL7LbEWauzv13aIpfmAu7Jv25x0sbraVtZe/bYAzazZYs2xj3V88C9npuZ/Q4gbFK0PpWiQEtuaj3z3ZkVWJBI/SzOrYhIradSMiTsIlSqBxUAkmepTl06xwPC1uzOoRTAP/C3/OYHXhBKQn235lXgQ3D9svd0/befZFAmzz1xYrn3OOPR5eAJQFnmtwjho6cCsiTshlxg667lW3IiIuzGFjA+zcuTNneNvY2Fi6du3Ks88+y8iRI7FarQBMmjSJ0NBQwsPD2bVrl6OiALYzbF55pKoKQETkLxxSAl9++SXvvvsu6em2fekfffQRAwYMYPbs2RiGwapVq4iKimLr1q3Mnz+f8ePH89577zkiioiI3IBDSqBChQpMnDgx5+9RUVE0bNgQgObNm7Nx40YiIyMJCQnBYrEQGBhIdnY2Z8+edUQcERG5DoeUQNu2bfHw+POYs2EYWC5fEOXj40NycjIpKSn4+v55ZeyV20VEJO/kyXjBbn85Bz81NRV/f398fX1JTU3Ndbufn86pFxHJS3lSArVr12bLli0ArF27luDgYOrXr8/69euxWq3Ex8djtVoJCAjIizgiInJZnlwnMGTIEIYPH8748eMJCgqibdu2uLu7ExwcTFhYGFarlREjRuRFFBER+QuXuU5ARESu5nQl0KhRI+69916zY4iIOJXixYvz9ddfX3W705WAiIjYj2YTFxFxYSoBEREXphIQEXFhKgERERemEhARcWEqARERF6YSuIa/zoWwb98+nn32WXr06EHv3r05c+YMALNmzeKZZ54hNDSUZcuWXfe5lixZQlhYWJ7kBvtkT0xMpF+/fnTr1o3w8HCOHj3qNNn37dtHly5d6Nq1K0OHDs2ZuyI/ZAewWq306dOHOXPmXPUc15t3I7/nvtHj8nv2K/Lj5xRunN1un1NDcpk6darRvn17o3PnzoZhGEa3bt2MvXv3GoZhGHPmzDE+/PBDIzEx0XjiiSeMjIwMIzk52WjevLlhtVqveq6oqCijZ8+eOc/lLNmHDBli/Pjjj4ZhGMamTZuM1atXO032l19+2VizZo1hGIYxaNAgY9WqVfki+xWffvqp0blzZ2P27NlXPc9LL71kbN682TAMwxg+fLjx888/O0XuGz0uv2c3jPz5Ob3iRtnt9TnVlsDf/H0uhPHjx1OrVi0AsrOz8fLyIiAggEWLFuHp6cmZM2fw8vLKGSr7inPnzjF+/HiGDRvmdNm3b9/OqVOn6NWrF0uWLMmZC8IZsteqVYukpCQMwyA1NTXXkOZmZgdYvnw5FouFhx566JrPc615N5wh9/Ue50j2yp5fP6dw8+z2+pyqBP7m73MhlC5dGrD9wGfOnEmvXr0A8PDwYObMmYSFhfHkk0/meo7s7Gzeeecdhg4dio+Pj1NlBzh+/Dj+/v5MmzaNsmXL8uWXXzpN9kqVKjFmzBgef/xxEhMTadSoUb7IfvDgQZYuXcrrr79+3ecxrjHvhjPkvt6/lSPZI3t+/pzeys/dXp9TlcAtWLZsGSNHjmTq1Km5hrvu3r0769at47fffmPz5s05t0dFRREbG8uoUaMYNGgQ0dHRjBkzxozot50doFixYrRs2RKAli1bsmfPnjzNfMWdZB8zZgyzZs1i+fLldOzYkbFjx+Z1bODq7IsWLeLUqVM899xzfP/990ybNo21a9fmesy15t3Ia3eS+1qPM8PtZs/Pn9Nb+bnb63OaJ0NJO7MffviBefPmMWPGDIoVKwbA4cOHGT9+PBMnTsTT05NChQrl+gDXqVOHH3/8EYC4uDgGDRrEO++84xTZARo0aMD//vc/OnbsyG+//UbVqlWdJnvRokVzZqwrXbo027dvz+vo18z+1ltv5SyfOHEiJUuWpHnz5rked2XejUaNGrF27VoaN26cl7HvOPe1HpfX7iR7fv6c3srP3V6fU20J3EB2djZjxowhNTWV/v3706NHD/7zn/8QFBREzZo1CQsLIzw8nLp169KwYUOio6MZNWqU2bGBu8s+ZMgQfvjhB8LDw1m3bh3//Oc/nSb76NGjGThwIN27d2f27NkMHDgwX2S/nr//3CdOnEhYWBiZmZm0bds2j1Lfee7bfZwj3M3P3Gx3+//FHp9TjSIqIuLCtCUgIuLCVAIiIi5MJSAi4sJUAiIiLkwlICLiwnSdgAgwduxYoqKiOH36NGlpaZQvX57ixYvnOl3v7bffJioqimHDhtGkSRNmzpzJkiVLcq7+bNq0Ka+88so1nz8lJYU2bdqwcuXKXFenduzYkfbt27NgwQJatWrF4MGDHftGRf5GJSCCbQUPEBERweHDh6+7Mn7zzTdp0qQJs2fP5vfff2f69Ol4eXmRmZnJ4MGDWb9+PSEhIVc9ztfXl0ceeYQVK1bQqVMnAPbs2YO/vz99+vQhICCAw4cPO+4NilyHdgeJ3IHZs2fzzjvv5Az25enpyYQJE3IKYMaMGTkXtU2fPh2ALl26sGjRopznWLhwYZ4OXyxyLdoSELkDSUlJOWPkrFy5kunTp5OWlkZwcDDPPPMMy5YtY/bs2QA8//zzhISEULduXc6fP8+JEycoUaIEGzduZOjQoWa+DRGVgMid8PHxISkpiWLFitG6dWtat27N2rVrWbZsGQcPHiQ+Pj5nNM3z588TGxtLUFAQoaGhLF68mHLlytGyZUsKFSpk7hsRl6fdQSJ3oFu3bnz44YdkZGQAtjFgIiMjsVgsBAUFUbVqVaZPn86MGTPo1KkTNWrUAODJJ59k5cqVeT6Tlcj1aEtA5A707NmTOXPm8Pzzz+Pm5kZKSgr16tVj0KBBlCpViiZNmtC1a1cyMjKoU6cOZcqUAWyjnAYFBXHmzBkqVapk7psQQQPIidyyt99+m3bt2l01pK893OysJBFH0e4gkdvw8ccfs2nTJrs+5/Lly5k6dapdn1PkVmlLQETEhWlLQETEhakERERcmEpARMSFqQRERFyYSkBExIX9P3PcY5qnND4SAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.interpolate import splev, splrep\n",
    "from scipy.interpolate import InterpolatedUnivariateSpline\n",
    "\n",
    "actions = np.array(actions)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(temperatures, actions, '.', label='data')\n",
    "plt.xlabel('T [GeV]')\n",
    "plt.ylabel('S/T')\n",
    "\n",
    "nuc = np.linspace(140,140,100)\n",
    "x = np.flip(temperatures)\n",
    "y = np.flip(actions)\n",
    "spl = InterpolatedUnivariateSpline(x, y)\n",
    "x2 = np.linspace(x[0], x[-1], 100)\n",
    "y2 = spl(x2)\n",
    "plt.plot(x2, nuc, 'k--', label='S/T = 140')\n",
    "plt.plot(x2, y2, label='spline')\n",
    "print('TC = ', np.around(TC, 2))\n",
    "#plt.title('Critical temperature = 119.37 GeV')\n",
    "plt.legend()\n",
    "sns.despine()\n",
    "\n",
    "def difference(x):\n",
    "    return np.abs(spl(x) - 140)\n",
    "\n",
    "TN, = fsolve(difference, TC-1)\n",
    "\n",
    "\n",
    "phiN, = fsolve(findPhiForTN, phiAtMin)\n",
    "\n",
    "derivative = spl.derivative()\n",
    "betaH = TN*derivative(TN)\n",
    "alpha = latentHeat(TN, phiN)\n",
    "print('TN = ', np.around(TN,2))\n",
    "print('beta/H: ', np.around(betaH))\n",
    "print('Latent heat: ', np.around(alpha,3))"
   ]
  }
 ],
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