The European Physical Journal B - Condensed Matter and Complex Systems

, Volume 20, Issue 2, pp 217–233

The Bethe lattice spin glass revisited

  • M. Mézard
  • G. Parisi

DOI: 10.1007/PL00011099

Cite this article as:
Mézard, M. & Parisi, G. Eur. Phys. J. B (2001) 20: 217. doi:10.1007/PL00011099

Abstract:

So far the problem of a spin glass on a Bethe lattice has been solved only at the replica symmetric level, which is wrong in the spin glass phase. Because of some technical difficulties, attempts at deriving a replica symmetry breaking solution have been confined to some perturbative regimes, high connectivity lattices or temperature close to the critical temperature. Using the cavity method, we propose a general non perturbative solution of the Bethe lattice spin glass problem at a level of approximation which is equivalent to a one step replica symmetry breaking solution. The results compare well with numerical simulations. The method can be used for many finite connectivity problems appearing in combinatorial optimization.

PACS. 75.10.Nr Spin-glass and other random models

Copyright information

© EDP Sciences, Springer-Verlag 2001

Authors and Affiliations

  • M. Mézard
    • 1
  • G. Parisi
    • 2
  1. 1.Laboratoire de Physique Théorique et Modèles Statistiques, Université Paris Sud, Bâtiment 100, 91405 Orsay Cedex, FranceFR
  2. 2.Dipartimento di Fisica, Sezione INFN and Unità INFM, Università di Roma “La Sapienza”, Piazzale Aldo Moro 2, 00185 Rome, ItalyIT