In the context of the $p$-spin spherical model, we introduce a method for the computation of the number of stationary points of any nature (minima, saddles, etc.) of the Thouless-Anderson-Palmer free energy. In doing this we clarify the ambiguities related to the approximations usually adopted in the standard calculations of the number of states in mean-field spin-glass models.

• Received 4 November 1997

DOI:https://doi.org/10.1103/PhysRevB.57.11251