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.
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Received 27 September 2000
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Mézard, M., Parisi, G. The Bethe lattice spin glass revisited. Eur. Phys. J. B 20, 217–233 (2001). https://doi.org/10.1007/PL00011099
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DOI: https://doi.org/10.1007/PL00011099