Tap Complexity, the Cavity Method and Supersymmetry

TL;DR

This paper computes the TAP complexity for the SK model using the cavity method, clarifies the physical meaning of parameters, and explores supersymmetry properties, addressing key theoretical issues.

Contribution

It introduces necessary modifications to the cavity method for TAP complexity and links supersymmetry to physical parameters in the BM theory.

Findings

Modified cavity method for TAP complexity

Physical interpretation of BM parameters

Supersymmetry Ward identities relate to cavity parameters

Abstract

We compute the Bray and Moore (BM) TAP Complexity for the Sherrington-Kirkpatrick model through the cavity method, showing that some essential modifications are needed with respect to the standard formulation of the method. This allows to understand various features recently discovered and to unveil at last the physical meaning of the parameters of the BM theory. We also reconsider the supersymmetric (SUSY) formulation of the problem finding that the BM solution satisfies some proper SUSY Ward identities that are different from the standard ones. The SUSY relationships encode the physical meaning of the parameters obtained through the cavity method. The problem of the vanishing prefactor is addressed showing how it can be avoided.