A Study of XY Model by Spin-dynamic simulation

We studied the 2-dimensional XY model through a spin-dynamic simulation, by introducing a classical rotation. The magnetization, energy, susceptibility, heat capacity and correlation length are derived and well consistent with Monte Carlo simulation results. We also studied the mean square displacement < (φ(t) − φ(0))2 > for the individual spin. It was found that under low temperature T < 1.2, the spin is oscillating around the balance point and the mean square displacement is zero. Under high temperature T > 1.2, however, the spin is rotating along the same direction. A linear relation < φ(t)2 >∝ t was found, which is consistent with Einstein diffusion equation.