Universality of the mean-field for the Potts model

DOI10.1007/s00440-016-0718-0zbMath1369.60066arXiv1508.03949OpenAlexW2963742450MaRDI QIDQ2363647

Sumit Mukherjee, Anirban Basak

Publication date: 25 July 2017

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

Full work available at URL: https://arxiv.org/abs/1508.03949

zbMATH Keywords

large deviationsPotts modelmean fieldIsing measurelog partition function

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) Large deviations (60F10) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (23)

A likelihood-ratio type test for stochastic block models with bounded degrees ⋮ Gaussian-width gradient complexity, reverse log-Sobolev inequalities and nonlinear large deviations ⋮ A Case Study on Stochastic Games on Large Graphs in Mean Field and Sparse Regimes ⋮ Taming correlations through entropy-efficient measure decompositions with applications to mean-field approximation ⋮ Replica symmetry in upper tails of mean-field hypergraphs ⋮ Upper tail of the spectral radius of sparse Erdös-Rényi graphs ⋮ Normal approximation and fourth moment theorems for monochromatic triangles ⋮ Fluctuations of subgraph counts in graphon based random graphs ⋮ Upper Tails for Edge Eigenvalues of Random Graphs ⋮ Fluctuations in mean-field Ising models ⋮ Nonlinear large deviations: beyond the hypercube ⋮ Detecting structured signals in Ising models ⋮ Inference in Ising models on dense regular graphs ⋮ Joint estimation of parameters in Ising model ⋮ Local convexity of the TAP free energy and AMP convergence for \(\mathbb{Z}_2\)-synchronization ⋮ Nonlinear large deviation bounds with applications to Wigner matrices and sparse Erdős-Rényi graphs ⋮ On the mean-field equations for ferromagnetic spin systems ⋮ Decomposition of mean-field Gibbs distributions into product measures ⋮ A transportation approach to the mean-field approximation ⋮ Spectral edge in sparse random graphs: upper and lower tail large deviations ⋮ The Second-Moment Phenomenon for Monochromatic Subgraphs ⋮ Monochromatic subgraphs in randomly colored graphons ⋮ Large deviations for the largest eigenvalue of Gaussian networks with constant average degree

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Convergent sequences of dense graphs. II. Multiway cuts and statistical physics
• Counting in two-spin models on \(d\)-regular graphs
• Ising models on power-law random graphs
• High-dimensional structure estimation in Ising models: local separation criterion
• Mean-field limits of the quantum Potts model
• Limit theorems for the empirical vector of the Curie-Weiss-Potts model
• Convergent sequences of dense graphs. I: Subgraph frequencies, metric properties and testing
• Ising models on locally tree-like graphs
• High-dimensional Ising model selection using \(\ell _{1}\)-regularized logistic regression
• Gibbs measures and phase transitions on sparse random graphs
• Asymptotic theory of finite dimensional normed spaces. With an appendix by M. Gromov: Isoperimetric inequalities in Riemannian manifolds
• Limit theorems for maximum likelihood estimators in the Curie-Weiss-Potts model
• Rigorous analysis of discontinuous phase transitions via mean-field bounds
• An \(L^{p}\) theory of sparse graph convergence. II: LD convergence, quotients and right convergence
• History of the Lenz-Ising Model 1920--1950: from Ferromagnetic to Cooperative Phenomena
• On rates of convergence in the Curie-Weiss-Potts model with an external field
• The spectral gap of random graphs with given expected degrees
• Extremal cuts of sparse random graphs
• Factor models on locally tree-like graphs
• The replica symmetric solution for Potts models on \(d\)-regular graphs
• Estimation in spin glasses: a first step
• The Parisi formula
• Nonlinear large deviations
• Efficiently Learning Ising Models on Arbitrary Graphs
• Polynomial-Time Approximation Algorithms for the Ising Model
• Complete analysis of phase transitions and ensemble equivalence for the Curie–Weiss–Potts model
• A New Class of Upper Bounds on the Log Partition Function
• The Spectra of Random Graphs with Given Expected Degrees
• The Largest Eigenvalue of Sparse Random Graphs
• Beitrag zur Theorie des Ferromagnetismus
• An 𝐿^{𝑝} theory of sparse graph convergence I: Limits, sparse random graph models, and power law distributions
• Spectral techniques applied to sparse random graphs
• Neural networks and physical systems with emergent collective computational abilities.
• Combinatorial approach to the interpolation method and scaling limits in sparse random graphs

This page was built for publication: Universality of the mean-field for the Potts model