Dynamic relaxation of topological defect at Kosterlitz-Thouless phase transition

TL;DR

This study investigates the dynamic relaxation of vortex states at the Kosterlitz-Thouless transition in the 2D XY model using Monte Carlo simulations, analyzing critical behavior and effects of quenched disorder.

Contribution

It introduces a pseudo-magnetization to analyze dynamic scaling and demonstrates how core disorder can change the universality class.

Findings

Critical exponents for pseudo-magnetization and Binder cumulant determined.

Disorder in vortex core can alter dynamic universality class.

Theoretical long-wave approximation calculations support simulation results.

Abstract

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 pseudo-magnetization 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 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. Further, theoretical calculations based on the long-wave approximation are presented.