Effects of quenched disorder in three-dimensional lattice ${\mathbb Z}_2$ gauge Higgs models

TL;DR

This study investigates how uncorrelated quenched disorder affects the phase diagram and critical behavior of three-dimensional ${f Z}_2$ gauge Higgs models, revealing disorder-dependent changes in universality classes and critical exponents.

Contribution

It provides a detailed analysis of the impact of site and plaquette quenched disorder on phase transitions and universality classes in 3D ${f Z}_2$ gauge Higgs models, identifying relevant and irrelevant disorder effects.

Findings

Random-plaquette disorder changes universality class along the topological transition line.

Random-site disorder destabilizes certain critical behaviors, leading to a different universality class.

Critical exponents vary depending on the type of disorder and transition line.

Abstract

We study the effects of uncorrelated quenched disorder to the phase diagram and continuous transitions of three-dimensional lattice ${\mathbb Z}_2$ gauge Higgs models. For this purpose, we consider two types of quenched disorder, associated with the sites and plaquettes of the cubic lattice. In both cases, for sufficiently weak disorder, the phase diagram remains similar to that of the pure system, showing two different phases (one of them being a topologically ordered phase), separated by two different continuous transition lines. However, the quenched disorder changes the universality classes of the critical behaviors along some of the transition lines. The random-plaquette disorder turns out to be relevant along the topological ${\mathbb Z}_2$ gauge transition line, so the critical behaviors belong to the different random-plaquette $\mathbb{Z}_2$ gauge (RP${\mathbb Z}_2$G) universality class with length-scale exponent $\nu=\nu_{\rm rp}\approx 0.82$; on the other hand, it turns out to be irrelevant along the other Ising$^\times$ transition line (a variant of the Ising transitions with a gauge-dependent order parameter), leaving unchanged its asymptotic critical behaviors with $\nu=\nu_{\cal I}\approx 0.63$. The random-site disorder leads to a substantially different scenario: it destabilizes the Ising$^\times$ critical behaviors of the pure model, changing them into those of the randomly-dilute Ising$^{\times}$ (RDI$^{\times}$) universality class with $\nu=\nu_{\rm rdi}\approx 0.68$, while the critical behaviors along the other ${\mathbb Z}_2$ gauge topological transition line remains stable, with $\nu=\nu_{\cal I}\approx 0.63$.