The Bethe lattice spin glass revisited

So far the problem of a spin glass on a Bethe lattice has been solved only at tile replica symmetric level, which is wrong in the spin glass phase. Be cause of some technical difficulties, attempts at deriving a replica symmet ry breaking solution have been confined to some perturbative regimes, high connectivity lattices or temperature close to the critical temperature. Usi ng the cavity method: we propose a general non perturbative solution of the Bethe lattice spill glass problem at a level of approximation which is equ ivalent to a one step replica symmetry breaking solution. Tile results comp are well with numerical simulations. The method can be used for many finite connectivity problems appearing in combinatorial optimization.