A Morita Type Proof of the Replica-Symmetric Formula for SK

DOI10.1007/978-3-030-29077-1_4zbMath1446.82083arXiv1809.07972OpenAlexW2974583905MaRDI QIDQ3296409

Erwin Bolthausen

Publication date: 7 July 2020

Published in: Statistical Mechanics of Classical and Disordered Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.07972

zbMATH Keywords

spin glassreplica symmetrysecond moment methodTAP equation

Mathematics Subject Classification ID

Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) (82D30) Symmetry breaking in quantum theory (81R40) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31)

Related Items (12)

Fluctuation results for multi-species Sherrington-Kirkpatrick model in the replica symmetric regime ⋮ The replica symmetric formula for the SK model revisited ⋮ Algorithmic pure states for the negative spherical perceptron ⋮ TAP approach for multispecies spherical spin glasses II: the free energy of the pure models ⋮ On the concavity of the TAP free energy in the SK model ⋮ The free energy of spherical pure \(p\)-spin models: computation from the TAP approach ⋮ Large scale stochastic dynamics. Abstracts from the workshop held September 11--17, 2022 ⋮ Local convexity of the TAP free energy and AMP convergence for \(\mathbb{Z}_2\)-synchronization ⋮ On the TAP equations via the cavity approach in the generic mixed \(p\)-spin models ⋮ The generalized TAP free energy. II ⋮ Dynamical approach to the TAP equations for the Sherrington-Kirkpatrick model ⋮ On convergence of the cavity and Bolthausen's TAP iterations to the local magnetization

Cites Work

• Unnamed Item
• An iterative construction of solutions of the TAP equations for the Sherrington-Kirkpatrick model
• On the TAP free energy in the mixed \(p\)-spin models
• The geometry of the Gibbs measure of pure spherical spin glasses
• The thermodynamic limit in mean field spin glass models
• Thouless-Anderson-Palmer equations for generic \(p\)-spin glasses
• The TAP-Plefka variational principle for the spherical SK model
• The Sherrington-Kirkpatrick Model
• Capacity lower bound for the Ising perceptron
• Mean Field Models for Spin Glasses

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