Locality of Spontaneous Symmetry Breaking and Universal Spacing Distribution of Topological Defects Formed Across a Phase Transition

TL;DR

This paper investigates the spatial distribution of topological defects formed during phase transitions, demonstrating how the Kibble-Zurek mechanism predicts defect densities and how defect interactions influence their spatial arrangements in different dimensions.

Contribution

It introduces a Poisson point process model for defect distribution based on KZM density and analyzes defect correlations and spacing in one and two dimensions through simulations.

Findings

Poisson process accurately models defect spacing in 2D superconductor

Short-distance defect correlations in 1D due to kink excluded volume

Suppression of defect-defect spatial correlations in 2D systems

Abstract

The crossing of a continuous phase transition results in the formation of topological defects with a density predicted by the Kibble-Zurek mechanism (KZM). We characterize the spatial distribution of point-like topological defects in the resulting nonequilibrium state and model it using a Poisson point process in arbitrary spatial dimension with KZM density. Numerical simulations in a one-dimensional $\phi^4$ theory unveil short-distance defect-defect corrections stemming from the kink excluded volume, while in two spatial dimensions, our model accurately describes the vortex spacing distribution in a strongly-coupled superconductor indicating the suppression of defect-defect spatial correlations.