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 et al., J. Phys. A 36, 1175 (2003)] and the other one breaking it [A. J. Bray and M. A. Moore, J. Phys. C 13, L469 (1980)]. We review the previews studies on the subject, linking different perspectives and pointing out some inadequacies and even inconsistencies in both solutions.

Complexity of the Sherrington-Kirkpatrick Model in the Annealed Approximation / Crisanti, Andrea; L., Leuzzi; Parisi, Giorgio; Rizzo, Tommaso. - In: PHYSICAL REVIEW. B, CONDENSED MATTER AND MATERIALS PHYSICS. - ISSN 1098-0121. - STAMPA. - 68:(2003), pp. 174401-1-174401-15. [10.1103/PhysRevB.68.174401]

Complexity of the Sherrington-Kirkpatrick Model in the Annealed Approximation

CRISANTI, Andrea;PARISI, Giorgio;RIZZO, TOMMASO
2003

Abstract

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 et al., J. Phys. A 36, 1175 (2003)] and the other one breaking it [A. J. Bray and M. A. Moore, J. Phys. C 13, L469 (1980)]. We review the previews studies on the subject, linking different perspectives and pointing out some inadequacies and even inconsistencies in both solutions.
2003
01 Pubblicazione su rivista::01a Articolo in rivista
Complexity of the Sherrington-Kirkpatrick Model in the Annealed Approximation / Crisanti, Andrea; L., Leuzzi; Parisi, Giorgio; Rizzo, Tommaso. - In: PHYSICAL REVIEW. B, CONDENSED MATTER AND MATERIALS PHYSICS. - ISSN 1098-0121. - STAMPA. - 68:(2003), pp. 174401-1-174401-15. [10.1103/PhysRevB.68.174401]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/252922
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