On Spin-Glass Complexity

TL;DR

This paper investigates the complexity of spin-glass models with supersymmetry, providing insights into the structure of solutions and suggesting the absence of supersymmetric contributions in certain models like Sherrington-Kirkpatrick.

Contribution

It offers a theoretical analysis of quenched complexity in spin-glass models with supersymmetry, extending to models with Full Replica Symmetry Breaking phases.

Findings

Consistent with numerical results, suggesting no supersymmetric contribution in SK model.

Applicable to models with Full Replica Symmetry Breaking, like the Ising p-spin below Gardner temperature.

Discusses solutions that break supersymmetry in the complexity landscape.

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.