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The Bethe lattice spin glass revisited | | Marc Mezard
; Giorgio Parisi
; | | Date: |
27 Sep 2000 | | Journal: | Eur. Phys. J. B 20, 217 (2001) | | Subject: | Disordered Systems and Neural Networks | cond-mat.dis-nn | | 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. | | Source: | arXiv, cond-mat/0009418 | | Services: | Forum | Review | PDF | Favorites | |
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