  Bethe lattice spins glasses are supposed to be marginally stable, i.e. their
equilibrium probability distribution changes discontinuously when we add an
external perturbation. So far the problem of a spin glass on a Bethe lattice
has been studied only using an approximation where marginally stability is not
present, which is wrong in the spin glass phase. Because of some technical
difficulties, attempts at deriving a marginally stable 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 approach to the Bethe lattice spin glass
problem using approximations that should be hopeful consistent with marginal
stability.
