Ordering Kinetics of Conserved XY Models

TL;DR

This study investigates the ordering kinetics of conserved XY models in two and three dimensions, confirming theoretical growth laws and analyzing structure factors through simulations and approximations.

Contribution

It provides simulation-based validation of theoretical growth laws and analyzes structure factors using a Gaussian closure approximation.

Findings

Growth law in 2D: L(t) ~ t^{1/4}

Growth law in 3D: L(t) ~ (t ln t)^{1/4}

Gaussian closure approximates structure factor well in 3D

Abstract

The zero-temperature ordering kinetics of conserved XY models in spatial dimensions $d=2$ and 3 is studied using cell dynamical simulations. The growth of the characteristic length scale $L(t)$ is fully consistent with recent theoretical predictions: $L(t) \sim t^{1/4}$ for $d=2$ and $L(t) \sim (t\ln t)^{1/4}$ for $d=3$. A gaussian closure approximation describes the form of the structure factor rather well for $d=3$.