On the stationary points of the TAP free energy

TL;DR

This paper presents a method to accurately count stationary points of the TAP free energy in the p-spin spherical model, clarifying previous ambiguities and improving understanding of the energy landscape in mean field spin glasses.

Contribution

It introduces a novel method for computing the number of stationary points of the TAP free energy, addressing ambiguities in standard approximations.

Findings

Provides a precise count of stationary points including minima and saddles.

Clarifies the role of approximations in traditional calculations.

Enhances understanding of the energy landscape in spin glass models.

Abstract

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 TAP 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.