  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 $T_{BKT}$ .
