# Ising spin glasses in dimension two; universality and non-universality

## TL;DR

This study investigates two-dimensional Ising spin glasses with various interaction distributions, finding that continuous distributions share a universality class with identical critical exponents, while discrete distributions form separate classes with different exponents.

## Contribution

It provides a comprehensive comparison of multiple 2D ISG models, establishing universality among continuous distributions and non-universality among discrete ones.

## Key findings

- Continuous distribution models share the same critical exponents.
- Discrete distribution models have different critical exponents from continuous ones.
- Discrete models exhibit non-zero η, indicating different universality classes.

## Abstract

Following numerous earlier studies, extensive simulations and analyses were made on the continuous interaction distribution Gaussian model and the discrete bimodal interaction distribution Ising Spin Glass (ISG) models in dimension two (P.H. Lundow and I.A. Campbell, Phys. Rev. E {\bf 93}, 022119 (2016)). Here we further analyse the bimodal and Gaussian data together with data on two other continuous interaction distribution 2D ISG models, the uniform and the Laplacian models, and three other discrete interaction distribution models, a diluted bimodal model, an "anti-diluted" model, and a more exotic symmetric Poisson model. Comparisons between the three continuous distribution models show that not only do they share the same exponent $\eta \equiv 0$ but that to within the present numerical precision they share the same critical exponent $\nu$ also, and so lie in a single universality class. On the other hand the critical exponents of the four discrete distribution models are not the same as those of the continuous distributions, and differ from one discrete distribution model to another. Discrete distribution ISG models in dimension two have non-zero values of the critical exponent $\eta$; they do not lie in a single universality class.