Tap Complexity, the Cavity Method and Supersymmetry

Details Tap Complexity, the Cavity Method and Supersymmetry Tap Complexity, the Cavity Method and Supersymmetry

2004-03-10

arxiv.org/abs/cond-mat/0403261v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

16 pages, Corrected Typos

Scientific paper

10.1088/0305-4470/38/15/005

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.

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