Unraveling critical dynamics: The formation and evolution of topological textures

TL;DR

This paper investigates the formation and evolution of topological textures during a nonequilibrium phase transition in a 2+1D classical O(3) model, revealing scaling behaviors that differ from traditional predictions and highlighting the importance of defect interactions.

Contribution

It demonstrates that late-time scaling laws in topological textures result from a competition between initial correlation lengths and ordering dynamics, extending understanding beyond the Kibble-Zurek mechanism.

Findings

Texture separation scales as τ^{0.39}

Texture width scales as τ^{0.46}

Significant defect network evolution occurs before the transition ends

Abstract

We study the formation of topological textures in a nonequilibrium phase transition of an overdamped classical O(3) model in 2+1 dimensions. The phase transition is triggered through an external, time-dependent effective mass, parameterized by quench timescale \tau. When measured near the end of the transition the texture separation and the texture width scale respectively as \tau^(0.39 \pm 0.02) and \tau^(0.46 \pm 0.04), significantly larger than \tau^(0.25) predicted from the Kibble-Zurek mechanism. We show that Kibble-Zurek scaling is recovered at very early times but that by the end of the transition the power-laws result instead from a competition between the length scale determined at freeze-out and the ordering dynamics of a textured system. In the context of phase ordering these results suggest that the multiple length scales characteristic of the late-time ordering of a textured system derive from the critical dynamics of a single nonequilibrium correlation length. In the context of defect formation these results imply that significant evolution of the defect network can occur before the end of the phase transition. Therefore a quantitative understanding of the defect network at the end of the phase transition generally requires an understanding of both critical dynamics and the interactions among topological defects.