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

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 $T_{BKT}$ .