Evidence for existence of many pure ground states in 3d $\pm J$ Spin Glasses

TL;DR

This paper provides numerical evidence that many pure ground states exist in three-dimensional $ ext{±}J$ Ising spin glasses, supporting the replica symmetry breaking picture.

Contribution

It introduces a computational approach combining genetic algorithms and cluster-exact approximation to analyze ground states in 3D spin glasses.

Findings

The distribution of overlaps $P(|q|)$ converges to a nonzero width with increasing size.

Multiple pure ground states are supported by the convergence of $P(|q|)$.

Numerical results suggest complex energy landscape with many states.

Abstract

Ground states of 3d EA Ising spin glasses are calculated for sizes up to $14^3$ using a combination of genetic algorithms and cluster-exact approximation . The distribution $P(|q|)$ of overlaps is calculated. For increasing size the width of $P(|q|)$ converges to a nonzero value, indicating that many pure ground states exist for short range Ising spin glasses.