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

TL;DR

This study uses simulation techniques to analyze static and dynamic properties of the 2D anisotropic Heisenberg model, revealing vortex behaviors and correlation functions that depend on anisotropy and temperature.

Contribution

It provides a numerical analysis of vortex behavior and correlation functions in the 2D anisotropic Heisenberg model, highlighting differences across a critical anisotropy value.

Findings

Vortex behavior varies with anisotropy parameter bb.

Out-of-plane correlation functions show a central peak above T_{BKT} for bb > bb_c.

Dynamic correlations differ depending on whether bb is below or above the critical value.

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 $\lambda$ lies below or above a critical value $\lambda_c$ . The in-plane and out-of-plane correlation functions ($S^{xx}$ and $S^{zz}$) were obtained numerically for $\lambda < \lambda_c$ and $\lambda > \lambda_c$ . We found that the out-of-plane dynamical correlation function exhibits a central peak for $\lambda > \lambda_c$ but not for $\lambda < \lambda_c$ at temperatures above $T_{BKT}$ .