Finite-temperature topological transitions in the presence of quenched uncorrelated disorder

TL;DR

This paper investigates how quenched uncorrelated disorder affects finite-temperature topological transitions in a 3D lattice ${ m Z}_2$ gauge model, revealing a new universality class.

Contribution

It demonstrates that weak quenched disorder induces a new topological universality class, differing from the pure model, consistent with Harris criterion predictions.

Findings

Disorder leads to a distinct topological universality class.

Critical behavior aligns with Harris criterion for relevance of disorder.

Topological transitions are characterized by the absence of a local order parameter.

Abstract

We address issues related to the presence of defects at finite-temperature topological transitions, in particular when defects are modeled in terms of further variables associated with a quenched disorder, corresponding to the limit in which the defect dynamics is very slow. As a paradigmatic model, we consider the classical three-dimensional lattice ${\mathbb Z}_2$ gauge model in the presence of quenched uncorrelated disorder associated with the plaquettes of the lattice, whose topological transitions are characterized by the absence of a local order parameter. We study the critical behaviors in the presence of weak disorder. We show that they belong to a new topological universality class, different from that of the lattice ${\mathbb Z}_2$ gauge models without disorder, in agreement with the Harris criterium for the relevance of uncorrelated quenched disorder when the pure system undergoes a continuous transition with positive specific-heat critical exponent.