Disordered Ising model with correlated frustration

Abstract

We consider the $\pm J$ Ising model on a cubic lattice with a gauge-invariant disorder distribution. Disorder depends on a parameter ${\beta }_G$ that plays the role of a chemical potential for the amount of frustration. We study the model at a specific value of the disorder parameter ${\beta }_G$, where frustration shows long-range correlations. We characterize the universality class, obtaining accurate estimates of the critical exponents: $\nu =0.655(15)$ and ${\eta }_q=1.05(5)$, where ${\eta }_q$ is the overlap susceptibility exponent.

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• Effects of quenched disorder in three-dimensional lattice ${\mathbb{Z}}_2$ gauge Higgs models
• Exact mapping of a spin glass with correlated disorder to the pure Ising model