Free energy in the generalized Sherrington-Kirkpatrick mean field model

Abstract

Recently Michel Talagrand gave a rigorous proof of the Parisi formula in the Sherrington-Kirkpatrick model. In this paper we build upon the methodology developed by Talagrand and extend his result to the class of SK type models in which the spins have arbitrary prior distribution on a bounded subset of the real line.

60 pages

References in corpus (3)

• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• The Thermodynamic Limit in Mean Field Spin Glass Models
• Free energy in the Sherrington-Kirkpatrick model with constrained magnetization

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• Guerra's interpolation using Derrida-Ruelle cascades
• Nonconvex interactions in mean-field spin glasses
• High-dimensional Gaussian fields with isotropic increments seen through spin glasses
• Free energy in spin glass models with conventional order
• On the unbalanced cut problem and the generalized Sherrington-Kirkpatrick model
• The ${\ell }^p$-Gaussian-Grothendieck problem with vector spins
• Hamilton-Jacobi equations from mean-field spin glasses
• Localization and free energy asymptotics in disordered statistical mechanics and random growth models
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• Thouless-Anderson-Palmer equations for the Ghatak-Sherrington mean field spin glass model