Strong universality and algebraic scaling in two-dimensional Ising spin glasses

TL;DR

This paper provides numerical evidence that various two-dimensional Ising spin glasses share a universal algebraic scaling behavior at low temperatures, indicating a single universality class despite different models.

Contribution

It demonstrates that different 2D Ising spin glass models exhibit the same algebraic scaling at low temperatures, suggesting a universal class and connecting it with a real space renormalization approach.

Findings

η ≈ 0 across models

ν ≈ 3.5 across models

Algebraic scaling confirmed for multiple models

Abstract

At zero temperature, two-dimensional Ising spin glasses are known to fall into several universality classes. Here we consider the scaling at low but non-zero temperature and provide numerical evidence that $\eta \approx 0$ and $\nu \approx 3.5$ in all cases, suggesting a unique universality class. This algebraic (as opposed to exponential) scaling holds in particular for the $\pm J$ model, with or without dilutions and for the plaquette diluted model. Such a picture, associated with an exceptional behavior at T=0, is consistent with a real space renormalization group approach. We also explain how the scaling of the specific heat is compatible with the hyperscaling prediction.