Microcanonical Monte Carlo simulations for the two-dimensional XY model

Abstract

The authors have carried out microcanonical Monte Carlo (MC) simulations for the two-dimensional (2D) classical XY model on a square lattice having 900 spins with periodic boundary conditions. The temperature dependence of the energy, specific heat, mean-square magnetization and vortex density show good agreement with the existing canonical MC simulation results. They thus demonstrate ergodicity in the microcanonical MC simulations for the 2D classical XY model. The maximum of the temperature derivative of the vortex density is found to occur at the temperature corresponding to the maximum of the specific heat.