  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.
