Ground-state clusters of two-, three- and four-dimensional +-J Ising spin glasses
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.
Keywords
Cite
@article{arxiv.cond-mat/9902120,
title = {Ground-state clusters of two-, three- and four-dimensional +-J Ising spin glasses},
author = {Alexander K. Hartmann},
journal= {arXiv preprint arXiv:cond-mat/9902120},
year = {2009}
}
Comments
large extensions, now 12 pages, 9 figures, 27 references