Replica symmetry breaking of the Ising spin-glass with finite connectivity

Pik Y. Lai, Y. Y. Goldschmidt

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14 Scopus citations

Abstract

The authors consider the Ising spin-glass on a lattice with finite connectivity (=M+1). Using the recent method of large connectivity expansions, the free energies at finite temperatures are evaluated numerically at first-step replica symmetry breaking (RSB). The 1/M expansion at finite temperature diverges as T0 as in the replica symmetric case but is well behaved for a larger range. The 1/M expansion at zero temperature is also calculated at higher steps of RSB. An expression for the free-energy expansion is derived for an arbitrary step of RSB up to order 1/M. Explicit numerical values at second-step RSB are obtained. From the results, they speculate that the divergence in the finite-temperature expansion might disappear for the exact infinite-step RSB solution. They also compare their results with the simulation results of graph bipartitioning.

Original languageEnglish
Article number029
Pages (from-to)3329-3340
Number of pages12
JournalJournal of Physics A: Mathematical and General
Volume23
Issue number14
DOIs
StatePublished - 1990

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