Numerical study of metastable states in Ising spin glasses

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