Dynamic relaxation of topological defect at Kosterlitz-Thouless phase transition

With Monte Carlo methods we study the dynamic relaxation of a vortex state at the Kosterlitz-Thouless phase transition of the two-dimensional XY model. A local pseudo-magnetization is introduced to characterize the symmetric structure of the dynamic systems. The dynamic scaling behavior of the pseudomagnetization and Binder cumulant is carefully analyzed, and the critical exponents are determined. To illustrate the dynamic effect of the topological defect, similar analysis for the dynamic relaxation with a spin-wave initial state is also performed for comparison. We demonstrate that a limited amount of quenched disorder in the core of the vortex state may alter the dynamic universality class. Furthermore, theoretical calculations based on the long-wave approximation are presented.