The goal of this project is to simulate physics in lattice systems. The first system we study here is the nearest neighbor Ising model. It can be shown analytically that the ferromagnetic state is the ground state of the nearest neighbor Ising model. The state is shown here.
The ferromagnetic state can be obtained in simulation by allowing the Monte Carlo to accept energy changes that both lower the energy as well as leave the energy unchanged. This does not always yield a ferromagnetic state, though. There are states that cannot be changed by this acceptance criterion. These states involve thick stripes that run all the way across the system. One such state is shown here.
We have attemped to use simulated annealing to find the ferromagnetic ground state of the system, but the system cannot reach the ground state with this method current. We are investigating this, because our intuition is that it should be possible to obtain the ground state with simulated annealing. Soon, we would also like to include animations that show the magnetic state changing as the temperature is lowered in simulated annealing.
The next model we will study is the classical Heisenberg model. We will study the nearest neighbor contribution.
After studying the Heisenberg model with nearest neighbor contributions, we will study the classical limit of the Kondo lattice model on the Kagome lattice. The classical limit is the Heisenberg model, which we obtain by calculating the second order perturbative energies. All couplings are kept in this calculation, not just nearest neighbor contributions. This is the work that was done in our Physical Review B paper Phase diagram of the Kondo lattice model on the kagome lattice.