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Effects of quenched disorder in three-dimensional lattice Z2 gauge Higgs models

Claudio Bonati1 and Ettore Vicari2

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Phys. Rev. E 114, 014107 – Published 6 July, 2026

DOI: https://doi.org/10.1103/q127-fnz1

Abstract

We study the effects of uncorrelated quenched disorder to the phase diagram and continuous transitions of three-dimensional lattice Z2 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 Z2 gauge transition line, so the critical behaviors belong to the different random-plaquette Z2 gauge (RPZ2G) universality class with length-scale exponent ν=νrp≈0.82; on the other hand, it turns out to be irrelevant along the other Ising× transition line (a variant of the Ising transitions with a gauge-dependent order parameter), leaving unchanged its asymptotic critical behaviors with ν=νI≈0.63. The random-site disorder leads to a substantially different scenario: it destabilizes the Ising× critical behaviors of the pure model, changing them into those of the randomly dilute Ising× (RDI×) universality class with ν=νRDI≈0.68, while the critical behaviors along the other Z2 gauge topological transition line remains stable, with ν=νI≈0.63.

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Phys. Rev. E 114, 014107– Published 6 July, 2026
  • Received 21 February 2026
  • Accepted 17 June 2026
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