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

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Show simple item record Kamppeter, Till Mertens, Franz G. Sánchez, Angel Domínguez-Adame, Francisco Bishop, Alan R. Gronbech-Jensen, Niels 2012-08-23T11:03:10Z 2012-08-23T11:03:10Z 1999-02
dc.identifier.bibliographicCitation The European Physical Journal B, vol. 7, n. 4, feb. 1999. Pp. 607-618
dc.identifier.issn 1434-6028 (print version)
dc.identifier.issn 1434-6036 (online version)
dc.description.abstract We study the e ects of nite 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 e ective di usion 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 nd 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 nd 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 e ects observed in the numerical simulations.
dc.description.sponsorship 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.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Springer
dc.title Finite temperature dynamics of vortices in the two dimensional anisotropic Heisenberg model
dc.type article
dc.description.status Publicado
dc.subject.eciencia Matemáticas
dc.identifier.doi 10.1007/s100510050653
dc.rights.accessRights openAccess
dc.type.version acceptedVersion
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