On Spin-Glass Complexity

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.

4 pages, 2 figures; Text changed in some parts, typos corrected, Refs. [17],[21] and [22] added, two Refs. removed

References in corpus (4)

• On the nature of the low-temperature phase in discontinuous mean-field spin glasses
• The Complexity of Ising Spin Glasses
• On the formal equivalence of the TAP and thermodynamic methods in the SK model
• Complexity of the Sherrington-Kirkpatrick Model in the Annealed Approximation

Cited by in corpus (18)

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• Complexity in Mean-Field Spin-Glass Models: Ising $p$-spin
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• Quenched Computation of the Complexity of the Sherrington-Kirkpatrick Model
• Coexistence of supersymmetric and supersymmetry-breaking states in spherical spin-glasses
• Distribution of rare saddles in the $p$-spin energy landscape
• On Equilibrium Dynamics of Spin-Glass Systems
• The density of stationary points in a high-dimensional random energy landscape and the onset of glassy behaviour
• Error threshold in optimal coding, numerical criteria and classes of universalities for complexity
• Tap Complexity, the Cavity Method and Supersymmetry
• Replica symmetry breaking, complexity and spin representation in the generalized random energy model
• The Complexity of Vector Spin Glasses
• Zero-Temperature Limit of the SUSY-breaking Complexity in Diluted Spin-Glass Models
• Incompleteness of the Thouless, Anderson, and Palmer mean-field description of the spin-glass phase
• Expected Number and Height Distribution of Critical Points of Smooth Isotropic Gaussian Random Fields
• Far-from-equilibrium complex landscapes