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On Spin-Glass Complexity

A. Crisanti·L. Leuzzi·G. Parisi·T. Rizzo
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Abstract

We study the quenched complexity in spin-glass mean-field models satisfying the Becchi-Rouet-Stora-Tyutin supersymmetry. The outcome of such study, consistent with recent numerical results, allows, in principle, to conjecture the absence of any supersymmetric contribution to the complexity in the Sherrington-Kirkpatrick model. The same analysis can be applied to any model with a Full Replica Symmetry Breaking phase, e.g. the Ising $p$-spin model below the Gardner temperature. The existence of different solutions, breaking the supersymmetry, is also discussed.

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A. Crisanti, L. Leuzzi, G. Parisi, T. Rizzo. 2003-12-01. On Spin-Glass Complexity. https://doi.org/10.1103/physrevlett.92.127203

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