Ground-state clusters of two-, three- and four-dimensional +-J Ising spin glasses

TL;DR

This paper computes and analyzes the ground-state configurations of +-J Ising spin glasses in two, three, and four dimensions, revealing exponential growth in the number of ground states and clusters with system size.

Contribution

It introduces a genetic cluster-exact approximation and a ballistic-search algorithm to identify and analyze ground-state clusters in high-dimensional spin glasses, extending previous methods.

Findings

Number of ground-state clusters diverges exponentially with system size.

Ground-state entropy per spin decreases with increasing dimension.

Number of distinct ground states grows exponentially with system size.

Abstract

A huge number of independent true ground-state configurations is calculated for two-, three- and four-dimensional +- J spin-glass models. Using the genetic cluster-exact approximation method, system sizes up to N=20^2,8^3,6^4 spins are treated. A ``ballistic-search'' algorithm is applied which allows even for large system sizes to identify clusters of ground states which are connected by chains of zero-energy flips of spins. The number of clusters n_C diverges with N going to infinity. For all dimensions considered here, an exponential increase of n_C appears to be more likely than a growth with a power of N. The number of different ground states is found to grow clearly exponentially with N. A zero-temperature entropy per spin of s_0=0.078(5)k_B (2d), s_0=0.051(3)k_B (3d) respectively s_0=0.027(5)k_B (4d) is obtained.