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

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