Comment on “Static and dynamic simulation in the classical two-dimensional anisotropic Heisenberg model”

Costa and Costa [Phys. Rev B 54, 994 (1996)] studied vortices in a two-dimensional easy-plane anisotropic ferromagnetic model. They found different vortex behaviors depending on whether the anisotropy parameter $\lambda$ is less than or greater than a critical value ${\lambda }_c,$ reproducing well-known results [Phys. Rev. B 39, 11 840 (1989)]. They claim that the out-of-plane dynamic correlation function $S^{\mathrm{zz}}(\mathbf{q},\omega )$ exhibits a central peak only for $\lambda >{\lambda }_c,$ where the static vortices are of the out-of-plane form, but not for $\lambda <{\lambda }_c,$ where the static vortices are planar. However, their data are physically inaccurate for such a conclusion.