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

Claudio Bonati1 and Ettore Vicari2

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Phys. Rev. E 113, 064123 – Published 10 June, 2026

DOI: https://doi.org/10.1103/v9j9-7gqs

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 Z2 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 topological universality class that differs from those of known statistical models, and in particular different from that of the lattice Z2 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.

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Phys. Rev. E 113, 064123– Published 10 June, 2026
  • Received 24 January 2026
  • Accepted 13 May 2026
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