Large deviations, a phase transition, and logarithmic Sobolev inequalities in the block spin Potts model

DOI10.1214/21-ECP397zbMath1479.60060arXiv2010.15542MaRDI QIDQ2064860

Holger Sambale, Holger Knöpfel, Matthias Loewe

Publication date: 6 January 2022

Published in: Electronic Communications in Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.15542

zbMATH Keywords

logarithmic Sobolev inequalityphase transitionlarge deviation principleblock spin Potts model

Mathematics Subject Classification ID

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

Related Items (2)

Energy landscape of the two-component Curie-Weiss-Potts model with three spins ⋮ Fluctuations of the magnetization in the block Potts model

Cites Work

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• Scaling limits for multi-species statistical mechanics mean-field models
• Entropy, large deviations, and statistical mechanics.
• Modified logarithmic Sobolev inequalities in discrete settings
• Limit theorems for the empirical vector of the Curie-Weiss-Potts model
• A diffusive strategic dynamics for social systems
• Large deviations techniques and applications.
• A conditional Curie-Weiss model for stylized multi-group binary choice with social interaction
• Fluctuations for block spin Ising models
• Fluctuation results for general block spin Ising models
• Concentration inequalities for bounded functionals via log-Sobolev-type inequalities
• Multi-group binary choice with social interaction and a random communication structure -- a random graph approach
• Logarithmic Sobolev inequalities for finite spin systems and applications
• Exact recovery in block spin Ising models at the critical line
• Two groups in a Curie-Weiss model
• Two groups in a Curie-Weiss model with heterogeneous coupling
• Macroscopic limit of a bipartite Curie-Weiss model: a dynamical approach
• Higher order concentration for functions of weakly dependent random variables
• Exact recovery in the Ising blockmodel
• Fluctuations of the magnetization for Ising models on dense Erdős-Rényi random graphs
• The thermodynamics of the Curie-Weiss model with random couplings
• Limit theorems for the bipartite Potts model
• Complete analysis of phase transitions and ensemble equivalence for the Curie–Weiss–Potts model
• Mixing of the Glauber dynamics for the ferromagnetic Potts model
• Bipartite Mean Field Spin Systems. Existence and Solution
• PARAMETER EVALUATION OF A SIMPLE MEAN-FIELD MODEL OF SOCIAL INTERACTION
• Modified log-Sobolev inequalities and two-level concentration
• Logarithmic Sobolev inequalities in discrete product spaces
• BEHAVIOR IN LARGE DIMENSIONS OF THE POTTS AND HEISENBERG MODELS
• Fluctuations of the magnetization for Ising models on Erdős–Rényi random graphs—the regimes of small p and the critical temperature ^*
• Large deviations
• Approximate tensorization of entropy at high temperature

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