A constructive mixing condition for 2-D Gibbs measures with random interactions

DOI10.1214/aop/1024404515zbMath0895.60097OpenAlexW2105373357MaRDI QIDQ1370229

Jacob Van Den Berg

Publication date: 20 September 1998

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1024404515

zbMATH Keywords

percolationcouplingGibbs measuresmixing random interactionsweak mixing property

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) Percolation (82B43) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (max. 100)

Random-cluster correlation inequalities for Gibbs fields ⋮ Uniqueness of Gibbs fields with unbounded random interactions on unbounded degree graphs ⋮ Mixing time of Markov chains for the 1-2 model

Cites Work

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• Gibbs measures and phase transitions
• Disagreement percolation in the study of Markov fields
• For 2-D lattice spin systems weak mixing implies strong mixing
• The uniqueness regime of Gibbs fields with unbounded disorder.
• A uniqueness condition for Gibbs measures, with application to the 2- dimensional Ising antiferromagnet
• The problem of uniqueness of a Gibbsian random field and the problem of phase transitions
• Uniqueness of a Gibes Field with Random Potential—An Elementary Approach

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