Numerical simulation of dynamics in theXYmodel

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Abstract
We study the dynamics of the classical two-dimensional XY model via numerical simulation using both microcanonical and Langevin equations of motion. We investigate three specific phenomena in this regard: the annealing of vortex defects during a quench from high to low temperature, the Brownian motion of an isolated vortex due to spin-wave interactions, and the temperature-dependent behavior of real-time spin-spin correlation functions. We compare the results of our simulations with simple theoretical models, whenever applicable.