Critical exponents of the binomial Ising Spin Glass in dimension four; non-universality

TL;DR

This study uses extensive simulations to analyze the critical behavior of the four-dimensional bimodal Ising Spin Glass, revealing that critical exponents vary with interaction distribution, indicating non-universality.

Contribution

It provides the first detailed estimation of critical exponents for 4d bimodal ISGs and demonstrates non-universality based on interaction distribution dependence.

Findings

Critical exponents $eta$, $ u$, $ heta$ are estimated.

Susceptibility and correlation length exponents depend on interaction distribution.

Critical exponents vary between different 4d ISG models.

Abstract

Extensive simulations are made on the bimodal Ising Spin Glass (ISG) in dimension four. The transition temperature is established using a combination of standard finite size scaling and of thermodynamic derivative peak data. Measurements in the thermodynamic limit regime are analysed so as to estimate critical exponents and confluent correction terms. Comparisons with results on other 4d ISGs show that the susceptibility and correlation length critical exponents $\gamma$ and $\nu$ depend on the form of the interaction distribution. From this observation it can be deduced that critical exponents are not universal in ISGs.