Publication: Finite temperature dynamics of vortices in the two dimensional anisotropic Heisenberg model
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1998
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Kamppeter, Till
Mertens, Franz G.
Sánchez, Angel
Bishop, A. R.
Grønbech-Jensen, N.
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Springer
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Abstract
We study the effects of finite temperature on the dynamics of non-planar vortices in the classical, two-dimensional anisotropic Heisenberg model with XY- or easy-plane symmetry. To this end, we analyze a generalized Landau-Lifshitz equation including additive white noise and Gilbert damping. Using a collective variable theory with no adjustable parameters we derive an equation of motion for the vortices with stochastic forces which are shown to represent white noise with an effective diffusion constant linearly dependent on temperature. We solve these stochastic equations of motion by means of a Green's function formalism and obtain the mean vortex trajectory and its variance. We find a non-standard time dependence for the variance of the components perpendicular to the driving force. We compare the analytical results with Langevin dynamics simulations and find a good agreement up to temperatures of the order of 25% of the Kosterlitz-Thouless transition temperature. Finally, we discuss the reasons why our approach is not appropriate for higher temperatures as well as the discreteness effects observed in the numerical simulations.
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© Springer International Publishing AG.
We thank Esteban Moro and Grant Lythe for discussions. Travel between Bayreuth and Madrid is supported by “Acciones Integradas Hispano-Alemanas”, a joint program of DAAD (Az. 314-AI) and DGES. Travel between Europe and Los Alamos is supported by NATO grant CRG 971090. Work at Madrid and Legan´es is supported by CICyT (Spain) grant MAT95-0325 and by DGES (Spain) grant PB96-0119. Work at Los Alamos is supported by the United States Department of Energy.
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[11]. The different signs appear due to the phase differences ±π/2, below Eq. (38).
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