How to count in hierarchical landscapes: a 'full' solution to mean-field complexity

Abstract

We derive the general solution for counting the stationary points of mean-field complex landscapes. It incorporates Parisi's solution for the ground state, as it should. Using this solution, we count the stationary points of two models: one with multi-step replica symmetry breaking, and one with full replica symmetry breaking.

References in corpus (4)

• Fractal free energy landscapes in structural glasses
• Following the evolution of glassy states under external perturbations: compression and shear-strain
• Shear yielding and shear jamming of dense hard sphere glasses
• Analytic continuation over complex landscapes

Cited by in corpus (8)

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• On Marginal Stability in Low Temperature Spherical Spin Glasses
• Landscape Complexity for the Empirical Risk of Generalized Linear Models: Discrimination between Structured Data
• Rényi complexity in mean-field disordered systems