Abnormal diffusion of a single vortex in the two dimensional XY model

TL;DR

This paper investigates the unusual diffusion behavior of a single vortex in the 2D XY model, revealing a decreasing mobility over time and modeling it with a diffusion-like equation that captures the core dynamics.

Contribution

It introduces a novel abnormal diffusion characterization of a vortex and develops a reduced model that accurately describes its dynamics.

Findings

Mobility decreases as 1/ln t over time.

The collective region radius grows as t^{1/2}.

The model conserves the key properties of the diffusion process.

Abstract

We study thermal diffusion dynamics of a single vortex in two dimensional XY model. By numerical simulations we find an abnormal diffusion such that the mobility decreases with time $t$ as $1/\ln t$. In addition we construct a one dimensional diffusion-like equation to model the dynamics and confirm that it conserves quantitative property of the abnormal diffusion. By analyzing the reduced model, we find that the radius of the collectively moving region with the vortex core grows as $R(t) \propto t^{1/2}$. This suggests that the mobility of the vortex is described by dynamical correlation length as $1/\ln R(t)$.