Publication: Finite temperature dynamics of vortices in the two dimensional anisotropic Heisenberg model
Loading...
Identifiers
Publication date
1999-02
Defense date
Advisors
Tutors
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
Impact
Export
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.
Description
Keywords
Bibliographic citation
The European Physical Journal B, vol. 7, n. 4, feb. 1999. Pp. 607-618