## 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 language | English |
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Article number | 029 |

Pages (from-to) | 3329-3340 |

Number of pages | 12 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 23 |

Issue number | 14 |

DOIs | |

State | Published - 1990 |