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.

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Cited by in corpus (8)

• On weak ergodicity breaking in mean-field spin glasses
• Arrangement of nearby minima and saddles in the mixed spherical energy landscapes
• When is the average number of saddle points typical?
• On the topology of solutions to random continuous constraint satisfaction problems
• Topological Phase Transitions in a Constrained Two-Qubit Quantum Control Landscape
• 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