Some properties of the phase diagram for mixed \(p\)-spin glasses

DOI10.1007/s00440-015-0691-zzbMath1370.60189arXiv1504.02731OpenAlexW2158822532MaRDI QIDQ525094

Ian Tobasco, Aukosh Jagannath

Publication date: 28 April 2017

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.02731

zbMATH Keywords

Ising modelfirst-order optimality conditionsphase boundarymixed \(p\)-spin glassesParisi functional

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) 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) Optimality conditions for problems involving randomness (49K45) Variational principles of physics (49S05) Optimality conditions for problems involving relations other than differential equations (49K21)

Related Items (17)

Fluctuation results for multi-species Sherrington-Kirkpatrick model in the replica symmetric regime ⋮ The replica symmetric formula for the SK model revisited ⋮ Spectral gap estimates in mean field spin glasses ⋮ On properties of the spherical mixed vector \(p\)-spin model ⋮ Generalized TAP Free Energy ⋮ Ultrametricity in spin glasses ⋮ On spin distributions for generic \(p\)-spin models ⋮ Replica symmetry breaking in multi-species Sherrington-Kirkpatrick model ⋮ The overlap gap property and approximate message passing algorithms for \(p\)-spin models ⋮ Bounds on the complexity of Replica Symmetry Breaking for spherical spin glasses ⋮ Low temperature asymptotics of spherical mean field spin glasses ⋮ On the unbalanced cut problem and the generalized Sherrington-Kirkpatrick model ⋮ Dynamical approach to the TAP equations for the Sherrington-Kirkpatrick model ⋮ Deep Boltzmann machines: rigorous results at arbitrary depth ⋮ On convergence of the cavity and Bolthausen's TAP iterations to the local magnetization ⋮ The overlap gap property in principal submatrix recovery ⋮ On the Almeida-Thouless transition line in the Sherrington-Kirkpatrick model with centered Gaussian external field

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Sherrington-Kirkpatrick model: an overview
• Some rigorous results on the Sherrington-Kirkpatrick spin glass model.
• Free energy of the spherical mean field model
• Derrida's generalised random energy models. I: Models with finitely many hierarchies
• On the high temperature phase of the Sherrington-Kirkpatrick model.
• The Parisi formula has a unique minimizer
• On properties of Parisi measures
• Parisi measures
• A question about the Parisi functional
• The Parisi formula for mixed \(p\)-spin models
• Limit theorems for sums of random exponentials
• The Parisi formula
• A dynamic programming approach to the Parisi functional
• Statistical Mechanics of Disordered Systems
• Quadratic replica coupling in the Sherrington–Kirkpatrick mean field spin glass model
• The Sherrington-Kirkpatrick Model
• FREE ENERGY IN THE GENERALIZED SHERRINGTON–KIRKPATRICK MEAN FIELD MODEL
• Mean Field Models for Spin Glasses

This page was built for publication: Some properties of the phase diagram for mixed \(p\)-spin glasses