Numerical study of metastable states in Ising spin glasses

We study numerically the structure of metastable states in the Sherrington-Kirkpatrick spin glass. We find that all nonparamagnetic stationary points of the free energy are organized into pairs, consisting of a minimum and an order 1 saddle, which coalesce in the thermodynamic limit. Within the annealed approximation, the entropic contribution of these states, that is the complexity, is compatible with the supersymmetry-breaking calculation performed by Bray and Moore [J. Phys. C 13, L469 (1980)]. This result indicates that the supersymmetry is spontaneously broken in the Sherrington-Kirkpatrick model.