Is there Kibble-Zurek scaling of topological defects in first-order phase transitions?

TL;DR

This paper investigates whether Kibble-Zurek scaling applies to topological defects in first-order phase transitions, finding that such scaling is only a rough approximation, but universal scaling for other properties exists.

Contribution

The study analyzes the applicability of Kibble-Zurek scaling to first-order phase transitions, revealing limitations and the existence of universal scaling for other properties.

Findings

Kibble-Zurek scaling is only a rough approximation in first-order transitions.

Universal scaling exists for properties other than defect density.

Scaling behavior differs fundamentally from continuous phase transitions.

Abstract

Kibble-Zurek scaling is the scaling of the density of the topological defects formed via the Kibble-Zurek mechanism with respect to the rate at which a system is cooled across a continuous phase transition. Recently, the density of the topological defects formed via the Kibble-Zurek mechanism was computed for a system cooled through a first-order phase transition instead of the usual continuous transitions. Here we address the problem of whether such defects generated across a first-order phase transition exhibit Kibble-Zurek scaling similar to the case in continuous phase transitions. We show that any possible Kibble-Zurek scaling for the topological defects can only be a very rough approximation due to an intrinsic field for the scaling. However, complete universal scaling for other properties does exist.