The Bethe lattice spin glass revisited

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