Spin Glass Computations and Ruelle's Probability Cascades

Abstract

We study the Parisi functional, appearing in the Parisi formula for the pressure of the SK model, as a functional on Ruelle's Probability Cascades (RPC). Computation techniques for the RPC formulation of the functional are developed. They are used to derive continuity and monotonicity properties of the functional retrieving a theorem of Guerra. We also detail the connection between the Aizenman-Sims-Starr variational principle and the Parisi formula. As a final application of the techniques, we rederive the Almeida-Thouless line in the spirit of Toninelli but relying on the RPC structure.

20 pages

References in corpus (4)

• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• Characterization of invariant measures at the leading edge for competing particle systems
• About the cavity fields in mean field spin glass models
• The replica symmetric region in the Sherrington-Kirkpatrick mean field spin glass model. The Almeida-Thouless line

Cited by in corpus (14)

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• Statistics at the tip of a branching random walk and the delay of traveling waves
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• On the structure of quasi-stationary competing particle systems
• Replica symmetry breaking in mean field spin glasses trough Hamilton-Jacobi technique
• An inference problem in a mismatched setting: a spin-glass model with Mattis interaction
• Interpolating the Sherrington-Kirkpatrick replica trick
• The Overlap Gap Property in Principal Submatrix Recovery
• A Multi-Scale Spin-Glass Mean-Field Model
• The full replica symmetry breaking in the Ising spin glass on random regular graph
• A Remark on the Infinite-Volume Gibbs Measures of Spin Glasses
• Notes on the polynomial identities in random overlap structures
• The Aizenman-Sims-Starr and Guerra's schemes for the SK model with multidimensional spins
• The full replica symmetry breaking solution in mean-field spin glass models