The Bethe lattice spin glass revisited

@misc{citeulike:2367426, 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.}, author = {Mezard, Marc and Parisi, Giorgio }, citeulike-article-id = {2367426}, comment = {* cited by their loop correction paper * p.3,4 derivation of BP update equations * getting free energy from BP equations}, eprint = {cond-mat/0009418}, keywords = {ising, message-passing, physics}, month = {Sep}, posted-at = {2008-02-13 00:15:51}, priority = {2}, title = {The Bethe lattice spin glass revisited}, url = {http://arxiv.org/abs/cond-mat/0009418}, year = {2000} }

TY - ELEC ID - citeulike:2367426 L3 - citeulike-article-id:2367426 TI - The Bethe lattice spin glass revisited N2 - 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. KW - ising KW - message-passing KW - physics N1 - * cited by their loop correction paper * p.3,4 derivation of BP update equations * getting free energy from BP equations AU - Mezard, Marc AU - Parisi, Giorgio PY - 2000/Sep/27/ UR - http://arxiv.org/abs/cond-mat/0009418 ER -