Thouless-Anderson-Palmer equations for generic \(p\)-spin glasses

DOI10.1214/18-AOP1307zbMath1426.82067arXiv1612.06359MaRDI QIDQ2327945

Aukosh Jagannath, Antonio Auffinger

Publication date: 8 October 2019

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.06359

zbMATH Keywords

spin glassesrandom measuresultrametricityTAPcluster decomposition

Mathematics Subject Classification ID

Gaussian processes (60G15) Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) (82D30) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31)

Related Items (20)

The replica symmetric formula for the SK model revisited ⋮ On properties of the spherical mixed vector \(p\)-spin model ⋮ The TAP-Plefka variational principle for the spherical SK model ⋮ TAP approach for multispecies spherical spin glasses II: the free energy of the pure models ⋮ Generalized TAP Free Energy ⋮ Dense Hebbian neural networks: a replica symmetric picture of supervised learning ⋮ 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 ⋮ On spin distributions for generic \(p\)-spin models ⋮ A Morita Type Proof of the Replica-Symmetric Formula for SK ⋮ TAP free energy, spin glasses and variational inference ⋮ Bethe states of random factor graphs ⋮ Spin systems on Bethe lattices ⋮ Dynamical approach to the TAP equations for the Sherrington-Kirkpatrick model ⋮ Thouless-Anderson-Palmer equations for the Ghatak-Sherrington mean field spin glass 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
• Spin glasses and Stein's method
• Construction of pure states in mean field models for spin glasses
• On spin distributions for generic \(p\)-spin models
• The Parisi ultrametricity conjecture
• The Ghirlanda-Guerra identities for mixed \(p\)-spin model
• On the structure of quasi-stationary competing particle systems
• The Parisi formula has a unique minimizer
• Hierarchical exchangeability of pure states in mean field spin glass models
• On properties of Parisi measures
• Approximate Ultrametricity for Random Measures and Applications to Spin Glasses
• The Sherrington-Kirkpatrick Model
• Random Fields and Geometry

This page was built for publication: Thouless-Anderson-Palmer equations for generic \(p\)-spin glasses