Ground-state behavior of the 3d +/-J random-bond Ising model

TL;DR

This study investigates the ground-state properties of the 3D $ ext{±}J$ random-bond Ising model, determining critical concentration and exponents using computational methods on large system sizes.

Contribution

It introduces a combined genetic algorithm and Cluster-Exact Approximation approach to analyze large 3D spin glass systems and accurately determine critical parameters.

Findings

Critical concentration $p_c=0.222 ext{±}0.005$ for loss of ferromagnetic order

Critical exponents $ u=1.1 ext{±}0.3$, $eta=0.2 ext{±}0.1$

Ground states calculated for systems up to $14^3$

Abstract

Large numbers of ground states of the three-dimensional $\pm J$ random-bond Ising model are calculated for sizes up to $14^3$ using a combination of a genetic algorithm and Cluster-Exact Approximation. Several quantities are calculated as function of the concentration $p$ of the antiferromagnetic bonds. The critical concentration where the ferromagnetic order disappears is determined using the Binder cumulant of the magnetization. A value of $p_c=0.222\pm 0.005$ is obtained. From the finite-size behavior of the Binder cumulant and the magnetization critical exponents $\nu=1.1 \pm 0.3$ and $\beta=0.2 \pm 0.1$ are calculated.