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We study the effects of finite temperature on the dynamics of non-planarvortices in the classical, two-dimensional anisotropic Heisenberg model withXY- or easy-plane symmetry. To this end, we analyze a generalizedLandau-Lifshitz equation including additive white noise and Gilbert damping.Using a collective variable theory with no adjustable parameters we derive anequation of motion for the vortices with stochastic forces which are shown torepresent white noise with an effective diffusion constant linearly dependenton temperature. We solve these stochastic equations of motion by means of aGreen's function formalism and obtain the mean vortex trajectory and itsvariance. We find a non-standard time dependence for the variance of thecomponents perpendicular to the driving force. We compare the analyticalresults with Langevin dynamics simulations and find a good agreement up totemperatures of the order of 25% of the Kosterlitz-Thouless transitiontemperature. Finally, we discuss the reasons why our approach is notappropriate for higher temperatures as well as the discreteness effectsobserved in the numerical simulations.Comment: 12 pages, 8 figures, accepted for publication in European Physical  Journal B (uses EPJ LaTeX

Finite temperature dynamics of vortices in the two dimensional anisotropic Heisenberg model