  The spontaneous supersymmetry-breaking that takes place in certain spin-glass
models signals a particular fragility in the structure of metastable states of
such systems. This fragility is due to the presence of at least one marginal
mode in the Hessian of the free energy, that makes the states highly
susceptible under external perturbations. The cavity method is a technique that
recursively describes the property of a system with N+1 spins in terms of those
of a system with N spins. To do so, the cavity method assumes a certain degree
of stability when adding a new spin to the system, i.e. it assumes that for a
generic choice of the parameters there is an one-to-one correspondence between
the metastable states of the system with N spins and the metastable states of
the system with N+1 spins. In systems where the supersymmetry is broken such a
correspondence does not exist, and an alternative formulation of the cavity
method must be devised. We introduce a generalized cavity approach that takes
care of this problem and we apply it to the computation of the probability
distribution of the local magnetizations in the Sherrington-Kirkpatrick model.
Our findings agree with the correct supersymmetry-breaking result.
