The critical behavior of three-dimensional Ising spin glass models

TL;DR

This study uses high-statistics Monte Carlo simulations to analyze the critical behavior of three-dimensional Ising spin-glass models, confirming they belong to a single universality class and estimating key critical exponents with high precision.

Contribution

The paper provides the first precise estimates of the critical exponents and the correction-to-scaling exponent for 3D Ising spin glasses, confirming universality across different models.

Findings

Models share the same universality class.

Estimated correction-to-scaling exponent mbda=1.0(1).

Critical exponents ppa=2.45(15), ta=-0.375(10).

Abstract

We perform high-statistics Monte Carlo simulations of three-dimensional Ising spin-glass models on cubic lattices of size L: the +- J (Edwards-Anderson) Ising model for two values of the disorder parameter p, p=0.5 and p=0.7 (up to L=28 and L=20, respectively), and the bond-diluted bimodal model for bond-occupation probability p_b = 0.45 (up to L=16). The finite-size behavior of the quartic cumulants at the critical point allows us to check very accurately that these models belong to the same universality class. Moreover, it allows us to estimate the scaling-correction exponent \omega related to the leading irrelevant operator: \omega=1.0(1). Shorter Monte Carlo simulations of the bond-diluted bimodal models at p_b=0.7 and p_b=0.35 (up to L=10) and of the Ising spin-glass model with Gaussian bond distribution (up to L=8) also support the existence of a unique Ising spin-glass universality class. A careful finite-size analysis of the Monte Carlo data which takes into account the analytic and the nonanalytic corrections to scaling allows us to obtain precise and reliable estimates of the critical exponents \nu and \eta: we obtain \nu=2.45(15) and \eta=-0.375(10).