Ordering temperatures and critical exponents in Ising spin glasses

TL;DR

This paper introduces a numerical criterion for accurately determining the ordering temperatures and critical exponents in Ising spin glasses, revealing non-zero transition temperatures and non-universal critical exponents.

Contribution

A new numerical method for precise estimation of transition temperatures and critical exponents in spin glasses, challenging universality assumptions.

Findings

Non-zero ordering temperature for 3D $ ext{±}J$ Ising spin glass

Critical exponents do not follow universality rules

Method yields results consistent with previous estimates

Abstract

We propose a numerical criterion which can be used to obtain accurate and reliable values of the ordering temperatures and critical exponents of spin glasses. Using this method we find an value of the ordering temperature for the $\pm J$ Ising spin glass in three dimensions which is definitely non-zero and in good agreement with previous estimates. We show that the critical exponents of three dimensional Ising spin glasses do not appear to obey the usual universality rules.