Static and dynamic simulation in the classical two-dimensional anisotropic Heisenberg model

Abstract

By using a simulated annealing approach, Monte Carlo and molecular-dynamics techniques we have studied static and dynamic behavior of the classical two-dimensional anisotropic Heisenberg model. We have obtained numerically that the vortex developed in such a model exhibit two different behaviors depending if the value of the anisotropy \ensuremath{\lambda} lies below or above a critical value ${\ensuremath{\lambda}}_{\mathit{c}}$. The in-plane and out-of-plane correlation functions (${\mathit{S}}^{\mathit{xx}}$ and ${\mathit{S}}^{\mathit{zz}}$) were obtained numerically for \ensuremath{\lambda}${\ensuremath{\lambda}}_{\mathit{c}}$ and \ensuremath{\lambda}\ensuremath{\gtrsim}${\ensuremath{\lambda}}_{\mathit{c}}$. We found that the out-of-plane dynamical correlation function exhibits a central peak for \ensuremath{\lambda}\ensuremath{\gtrsim}${\ensuremath{\lambda}}_{\mathit{c}}$ but not for \ensuremath{\lambda}${\ensuremath{\lambda}}_{\mathit{c}}$ at temperatures above ${\mathit{T}}_{\mathrm{KT}}$. \textcopyright{} 1996 The American Physical Society.