Monte Carlo Simulations of Spin-Lattice Models on the Sphere

Abstract

We have now introduced most of the components we need, and with an understanding of how to conduct each experiment we can set up a Monte Carlo simulator. Pick a mesh size N, pick an inverse temperature β, and conduct a large number of sweeps. Each sweep consists of N experiments. Each experiment consists of picking three distinct sites and attempting to vary their strength as described in the above section. The change in enthalpy ΔH from an experiment is calculated, and a random number r is drawn from the interval [0, 1]; the change in site values is accepted if r is less than exp(−βΔH) and is rejected otherwise.