Ground-state landscape of 2d +-J Ising spin glasses

TL;DR

This study computes numerous ground states of 2D ±J Ising spin glasses up to size 40^2, revealing a complex landscape that challenges simpler models and shows non-ultrametric organization.

Contribution

It introduces a combined genetic algorithm and Cluster-Exact Approximation method to analyze the ground-state landscape of 2D spin glasses, providing new insights into their complex organization.

Findings

Ground-state energy extrapolated to e=-1.4015(3) for infinite system

Mean-field picture better describes the landscape than droplet-scaling model

Ground states are not organized in an ultrametric fashion

Abstract

Large numbers of ground states of two-dimensional Ising spin glasses with periodic boundary conditions in both directions are calculated for sizes up to 40^2. A combination of a genetic algorithm and Cluster-Exact Approximation is used. For each quenched realization of the bonds up to 40 independent ground states are obtained. For the infinite system a ground-state energy of e=-1.4015(3) is extrapolated. The ground-state landscape is investigated using a finite-size scaling analysis of the distribution of overlaps. The mean-field picture assuming a complex landscape describes the situation better than the droplet-scaling model, where for the infinite system mainly two ground states exist. Strong evidence is found that the ground states are not organized in an ultrametric fashion in contrast to previous results for three-dimensional spin glasses.