Critical exponents in Ising spin glasses

TL;DR

This paper accurately determines the critical exponents and transition temperatures for Ising Spin Glasses in four dimensions, revealing non-universality depending on interaction distribution, and confirms similar findings in three dimensions.

Contribution

It provides precise critical exponents for 4D Ising Spin Glasses and demonstrates non-universality based on interaction distribution, extending understanding from 3D results.

Findings

Critical exponents vary with interaction distribution

Non-universality observed at Ising spin glass transitions

Results consistent with previous 3D numerical data

Abstract

We determine accurate values of ordering temperatures and critical exponents for Ising Spin Glass transitions in dimension 4, using a combination of finite size scaling and non-equilibrium scaling techniques. We find that the exponents $\eta$ and $z$ vary with the form of the interaction distribution, indicating non-universality at Ising spin glass transitions. These results confirm conclusions drawn from numerical data for dimension 3.