The Bethe lattice spin glass revisited

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

The European Physical Journal B: Condensed Matter and Complex Systems, 2001, vol. 20, issue 2, 217-233

Abstract: 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.

Keywords: PACS.; 75.10.Nr; Spin-glass; and; other; random; models (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (11)

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DOI: 10.1007/PL00011099

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