Complexity of the Sherrington-Kirkpatrick Model in the Annealed Approximation

Details Complexity of the Sherrington-Kirkpatrick Model in the Annealed Approximation Complexity of the Sherrington-Kirkpatrick Model in the Annealed Approximation

2003-07-03

arxiv.org/abs/cond-mat/0307082v1

Phys. Rev. B, 68 (2003) 174401

Physics

Condensed Matter

Disordered Systems and Neural Networks

20 pages, 4 figures

Scientific paper

10.1103/PhysRevB.68.174401

A careful critical analysis of the complexity, at the annealed level, of the Sherrington-Kirkpatrick model has been performed. The complexity functional is proved to be always invariant under the Becchi-Rouet-Stora-Tyutin supersymmetry, disregarding the formulation used to define it. We consider two different saddle points of such functional, one satisfying the supersymmetry [A. Cavagna {\it et al.}, J. Phys. A {\bf 36} (2003) 1175] and the other one breaking it [A.J. Bray and M.A. Moore, J. Phys. C {\bf 13} (1980) L469]. We review the previews studies on the subject, linking different perspectives and pointing out some inadequacies and even inconsistencies in both solutions.

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