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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.
Crisanti et al. (Mon,) studied this question.