On the Motion of Vortex Pairs in the Anisotropic Heisenberg Model
We consider a classical 2D Heisenberg model with easy-plane symmetry. Koster-litz and Thouless1 showed that such a system has a topological phase transition: at low temperatures there exist bound vortex pairs which start to dissociate above a critical temperature T KT Just above T KT we can assume that there are only a few free vortices which move ballistically between their interactions. A model of dynamics built on such a “vortex gas” has been constructed assuming a Gaussian velocity distribution. Here we use effective equations of motion for the collective (center-of-mass) vortex variables and compare these analytical results of vortex-vortex and vortex-anitvortex interactions with molecular dynamics simulations of the full spin system.3 We investigate both ferromagnets (FM) and antiferromagnets (AFM) with an anisotropy parameter λ varying from zero to one.
KeywordsStatic Force Anisotropy Parameter Elsevier Science Publisher Vortex Pair Heisenberg Model
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