The weak limit of Ising models on locally tree-like graphs

DOI10.1007/s00440-010-0315-6zbMath1242.82012arXiv0912.0719OpenAlexW2013464260MaRDI QIDQ664346

Allan Sly, Elchanan Mossel, Andrea Montanari

Publication date: 1 March 2012

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

Full work available at URL: https://arxiv.org/abs/0912.0719

zbMATH Keywords

phase transitionIsing modelGibbs measureIsing measure

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Phase transitions (general) in equilibrium statistical mechanics (82B26) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items

Ising critical behavior of inhomogeneous Curie-Weiss models and annealed random graphs, Glauber dynamics for Ising models on random regular graphs: cut-off and metastability, Ising models on power-law random graphs, Local weak convergence for sparse networks of interacting processes, Finite-size scaling, phase coexistence, and algorithms for the random cluster model on random graphs, Free energy, Gibbs measures, and Glauber dynamics for nearest-neighbor interactions, Factor models on locally tree-like graphs, ADDITIVITY PROPERTIES OF SOFIC ENTROPY AND MEASURES ON MODEL SPACES, The replica symmetric solution for Potts models on \(d\)-regular graphs, Metastability of the Ising model on random regular graphs at zero temperature, Evolutionary potential games on lattices, Gibbs measures over locally tree-like graphs and percolative entropy over infinite regular trees, Duality and free energy analyticity bounds for few-body Ising models with extensive homology rank, Local convergence of random graph colorings, Quenched central limit theorems for the Ising model on random graphs, Ising model on trees and factors of IID, Weighted enumeration of spanning subgraphs in locally tree-like graphs, The Lanford–Ruelle theorem for actions of sofic groups

Cites Work

• Rounding effects of quenched randomness on first-order phase transitions
• Ising models on locally tree-like graphs
• Gibbs measures and phase transitions
• The central limit theorem and the problem of equivalence of ensembles
• Metastates in disordered mean-field models: Random field and Hopfield models
• Processes on unimodular random networks
• Translation invariant Gibbs states for the Ising model
• Phase transitions on nonamenable graphs
• Percolation and number of phases in the two-dimensional Ising model
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item