Phase Transition in the Three-Dimensional $\pm J$ Ising Spin Glass

TL;DR

This study uses Monte Carlo simulations to analyze the phase transition in the three-dimensional $ ext{±}J$ Ising spin glass, providing evidence for a finite transition temperature with ordering below it, and refining previous estimates.

Contribution

It offers improved estimates of the transition temperature and critical exponents for the 3D $ ext{±}J$ Ising spin glass using larger system sizes and better statistics.

Findings

Evidence for a finite transition temperature $T_c$

Estimate of $T_c$ is lower than previous studies

Correlation length exponent $ u$ is higher than earlier estimates

Abstract

We have studied the three-dimensional Ising spin glass with a $\pm J$ distribution by Monte Carlo simulations. Using larger sizes and much better statistics than in earlier work, a finite size scaling analysis shows quite strong evidence for a finite transition temperature, $T_c$, with ordering below $T_c$. Our estimate of the transition temperature is rather lower than in earlier work, and the value of the correlation length exponent, $\nu$, is somewhat higher. Because there may be (unknown) corrections to finite size scaling, we do not completely rule out the possibility that $T_c = 0$ or that $T_c$ is finite but with no order below $T_c$. However, from our data, these possibilities seem less likely.