The TAP-Plefka variational principle for the spherical SK model

DOI10.1007/s00220-019-03304-yzbMath1419.82069arXiv1802.05782OpenAlexW3105662517WikidataQ128443512 ScholiaQ128443512MaRDI QIDQ2414718

David Belius, Nicola Kistler

Publication date: 17 May 2019

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.05782

zbMATH Keywords

Sherrington-Kirkpatrick modelThouless-Anderson-Palmer approach

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)

Related Items (14)

The replica symmetric formula for the SK model revisited ⋮ TAP approach for multispecies spherical spin glasses II: the free energy of the pure models ⋮ Generalized TAP Free Energy ⋮ 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 ⋮ The TAP free energy for high-dimensional linear regression ⋮ Ultrametricity in spin glasses ⋮ Local convexity of the TAP free energy and AMP convergence for \(\mathbb{Z}_2\)-synchronization ⋮ Shattering versus metastability in spin glasses ⋮ On the TAP equations via the cavity approach in the generic mixed \(p\)-spin models ⋮ The generalized TAP free energy. II ⋮ A Morita Type Proof of the Replica-Symmetric Formula for SK ⋮ On convergence of the cavity and Bolthausen's TAP iterations to the local magnetization ⋮ Marginals of a spherical spin Glass model with correlated disorder

Cites Work

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• Legendre duality of spherical and Gaussian spin glasses
• An iterative construction of solutions of the TAP equations for the Sherrington-Kirkpatrick model
• Fluctuations of the free energy of the spherical Sherrington-Kirkpatrick model
• Spin glasses and Stein's method
• Some rigorous results on the Sherrington-Kirkpatrick spin glass model.
• Free energy of the spherical mean field model
• The geometry of the Gibbs measure of pure spherical spin glasses
• Broken replica symmetry bounds in the mean field spin glass model
• The Parisi ultrametricity conjecture
• Thouless-Anderson-Palmer equations for generic \(p\)-spin glasses
• The Parisi formula
• The Sherrington-Kirkpatrick Model
• Random Matrices and Complexity of Spin Glasses

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