The free energy of spherical pure \(p\)-spin models: computation from the TAP approach

DOI10.1007/s00440-023-01200-0zbMath1517.82043arXiv2101.04352OpenAlexW3119423896MaRDI QIDQ6101235

Eliran Subag

Publication date: 20 June 2023

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

Full work available at URL: https://arxiv.org/abs/2101.04352

zbMATH Keywords

free energyTAP approachspherical spin models

Mathematics Subject Classification ID

Random fields (60G60) Gaussian processes (60G15) Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) (82D30) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (3)

On a nonhierarchical generalization of the perceptron GREM ⋮ Local convexity of the TAP free energy and AMP convergence for \(\mathbb{Z}_2\)-synchronization ⋮ Replica-symmetry breaking transitions in the large deviations of the ground-state of a spherical spin-glass

Cites Work

• Unnamed Item
• The Aizenman-Sims-Starr scheme and Parisi formula for mixed \(p\)-spin spherical models
• 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
• Parisi formula, disorder chaos and fluctuation for the ground state energy in the spherical mixed \(p\)-spin models
• Low temperature asymptotics of spherical mean field spin glasses
• Parisi formula for the ground state energy in the mixed \(p\)-spin model
• Some rigorous results on the Sherrington-Kirkpatrick spin glass model.
• Free energy of the spherical mean field model
• The Sherrington-Kirkpatrick model of spin glasses and stochastic calculus: The high temperature case
• The Sherrington-Kirkpatrick model: A challenge for mathematicians
• Rigorous low-temperature results for the mean field \(p\)-spins interaction model
• On the TAP free energy in the mixed \(p\)-spin models
• The geometry of the Gibbs measure of pure spherical spin glasses
• The complexity of spherical \(p\)-spin models: a second moment approach
• The thermodynamic limit in mean field spin glass models
• Broken replica symmetry bounds in the mean field spin glass model
• The Parisi ultrametricity conjecture
• Convergence of the free energy for spherical spin glasses
• The generalized TAP free energy. II
• Phase transition in the spiked random tensor with Rademacher prior
• The extremal process of critical points of the pure \(p\)-spin spherical spin Glass model
• The TAP-Plefka variational principle for the spherical SK model
• Complexity of random smooth functions on the high-dimensional sphere
• The Parisi formula for mixed \(p\)-spin models
• The Parisi formula
• Replica symmetry breaking and the nature of the spin glass phase
• A Morita Type Proof of the Replica-Symmetric Formula for SK
• On the formal equivalence of the TAP and thermodynamic methods in the SK model
• The Sherrington-Kirkpatrick Model
• Random Matrices and Complexity of Spin Glasses
• Following the Ground States of <scp>Full‐RSB</scp> Spherical Spin Glasses
• Geometry and Temperature Chaos in Mixed Spherical Spin Glasses at Low Temperature: The Perturbative Regime
• Mean Field Models for Spin Glasses

This page was built for publication: The free energy of spherical pure \(p\)-spin models: computation from the TAP approach