Vortex Dynamics in a Coarsening Two Dimensional XY Model

TL;DR

This paper investigates vortex dynamics during coarsening in a 2D XY model, numerically analyzing vortex velocity distributions and confirming theoretical predictions about their scaling behavior over time.

Contribution

It provides the first detailed numerical analysis of vortex velocity distributions in a 2D coarsening XY model, validating theoretical scaling laws.

Findings

Vortex velocity distribution scales with the average vortex speed.

The average vortex speed decreases as t^{-x} with x near 1/2.

The distribution exhibits a large speed algebraic tail in agreement with theory.

Abstract

The vortex velocity distribution function for a 2-dimensional coarsening non-conserved O(2) time-dependent Ginzburg-Landau model is determined numerically and compared to theoretical predictions. In agreement with these predictions the distribution function scales with the average vortex speed which is inversely proportional to t^x, where t is the time after the quench and x is near to 1/2. We find the entire curve, including a large speed algebraic tail, in good agreement with the theory.