Topological transitions in the presence of quenched uncorrelated disorder

TL;DR

The paper studies how quenched, uncorrelated disorder affects topological, gauge-theoretic transitions lacking a local order parameter, using the 3D Z2 RPGM as a paradigmatic model. It demonstrates that weak disorder is relevant by the Harris criterion and identifies a new topological universality class characterized by a drift of the correlation-length exponent to $\nu \approx 0.82$, with $\alpha<0$. The work provides robust finite-size scaling analysis of gauge-invariant energy cumulants $B_k$ and discusses multicritical behavior near the Nishimori point, as well as extensions to Z_N gauge models. These results advance understanding of disorder effects at topological transitions and offer a framework for predicting universality changes in disordered gauge systems.

Abstract

We address issues related to the presence of defects at 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 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.

Figures (6)

• Figure 1: The expected phase diagram of the 3D RPGM, see Refs. WHP-03OAIM-04. The continuous line separates the deconfined phase, at small $K^{-1}$ and $q$, from the confined phase, while the dashed line denotes the Nishimori line. The black dot $N$ represents the point where the deconfinement transition line intersects the Nishimori line, and the value of $q$ at this point is denoted by $q_N$ in the main text.
• Figure 2: Data for the second cumulants $B_2$, proportional to the specific heat, across the topological transition for $q=0.015$.
• Figure 3: Data for the third cumulant $B_3$ for $q=0.015$, across the topological transition around $K\approx 0.89$. Continuous lines for $L=12, 16, 20$ are drawn just to guide the eye.
• Figure 4: Scaling of third cumulant $B_3$ for $q=0.015$, obtained by plotting $L^{3-3/\nu} B_3$ versus $(K-K_c)L^{1/\nu}$ with our optimal estimates $K_c=0.8940$ and $\nu=0.82$.
• Figure 5: Data for the third cumulant $B_3$ for $K=1$, across the topological transition around $q\approx 0.022$. Continuous lines for $L=12, 16, 20$ are drawn just to guide the eye.