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.

large extensions, now 12 pages, 9 figures, 27 references

References in corpus (4)

• Scaling of stiffness energy for 3d +/-J Ising spin glasses
• Calculation of ground states of four-dimensional +or- J Ising spin glasses
• A new method for analyzing ground-state landscapes: ballistic search
• Ground-state landscape of 2d +-J Ising spin glasses

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