# Three-dimensional universality class of Ising model with power-law-correlated critical disorder

## TL;DR

This study uses large-scale Monte Carlo simulations to investigate the universality class of the 3D Ising model with power-law-correlated disorder, revealing new critical exponents and complex phase transition behaviors.

## Contribution

It introduces a novel method for generating correlated disorder in the 3D Ising model and provides empirical evidence for a new universality class with distinct critical exponents.

## Key findings

- Identifies a new universality class with specific critical exponents.
- Shows disorder-averaged quantities can have peaks at two temperatures.
- Demonstrates a layer model with spatially separated bonds exhibits multiple phase transitions.

## Abstract

We use large-scale Monte Carlo simulations to test the Weinrib-Halperin criterion that predicts new universality classes in the presence of sufficiently slowly decaying power-law-correlated quenched disorder. While new universality classes are reasonably well established, the predicted exponents are controversial. We propose a method of growing such correlated disorder using the three-dimensional Ising model as benchmark systems both for generating disorder and studying the resulting phase transition. Critical equilibrium configurations of a disorder-free system are used to define the two-value distributed random bonds with a small power-law exponent given by the pure Ising exponent. Finite-size scaling analysis shows a new universality class with a single phase transition, but the critical exponents $\nu_d=1.13(5), \eta_d=0.48(3)$ differ significantly from theoretical predictions. We find that depending on details of the disorder generation, disorder-averaged quantities can develop peaks at two temperatures for finite sizes. Finally, a layer model with the two values of bonds spatially separated to halves of the system genuinely has multiple phase transitions and thermodynamic properties can be flexibly tuned by adjusting the model parameters.