# Disordered Ising model with correlated frustration

## TL;DR

This paper investigates a disordered Ising model with correlated frustration, analyzing its critical behavior and universality class through numerical estimates of critical exponents at a specific disorder parameter.

## Contribution

It introduces a gauge-invariant disorder distribution with long-range correlations and provides precise estimates of critical exponents for this model.

## Key findings

- Critical exponents estimated: ν = 0.655(15), η_q = 1.05(5).
- Frustration exhibits long-range correlations at the studied parameter.
- Model belongs to a specific universality class characterized by these exponents.

## 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.