Critical density of topological defects upon a continuous phase transition

TL;DR

This study uses Monte Carlo simulations to investigate whether the density of topological defects reaches a universal value at continuous phase transitions across various 2D models, confirming the hypothesis.

Contribution

It provides the first comprehensive numerical evidence that topological defect densities are universal at phase transitions in diverse 2D systems.

Findings

Defect densities are consistent across different models and lattice types.

Universal defect density observed at phase transition points.

Results support the hypothesis of universality in defect densities.

Abstract

Using extensive Monte Carlo simulations, we test the hypothesis that the density of corresponding topological defects has an universal value at the temperature of a continuous phase transition. We consider several simple two-dimensional models where domain walls, vortices, so-called $\mathbb{Z}_2$ vortices or their combinations are presented. These topological defects are relevant correspondingly to an Ising second-order phase transition, a Berezinskii-Kosterlitz Thouless transition and an explicit crossover. We compare results for square and triangular lattices as well as for the complicated situation when two types of defects are presented and two transitions occur separated in temperature. All considered cases demonstrate consentient results confirming the hypothesis.