Strict inequality for critical values of Potts models and random-cluster processes

DOI10.1007/BF02097229zbMath0783.60100OpenAlexW1973744336MaRDI QIDQ1313278

Geoffrey R. Grimmett, C. E. Bezuidenhout, Harry Kesten

Publication date: 14 March 1994

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02097229

zbMATH Keywords

FKG inequalitypercolation theoryrandom-cluster representationferromagnetic Potts model

Mathematics Subject Classification ID

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

Related Items (16)

Mixed percolation as a bridge between site and bond percolation. ⋮ A note on exponential decay in the random field Ising model ⋮ The random cluster process ⋮ Potts models and random-cluster processes with many-body interactions ⋮ Influence and sharp-threshold theorems for monotonic measures ⋮ Infrared bound and mean-field behaviour in the quantum Ising model ⋮ The symbiotic contact process ⋮ Sharp thresholds for the random-cluster and Ising models ⋮ Strict inequalities of critical values in continuum percolation ⋮ Ultrasensitivity and sharp threshold theorems for multisite systems ⋮ Self-Avoiding Walks and Connective Constants ⋮ On the truncation of systems with non-summable interactions ⋮ The self-dual point of the two-dimensional random-cluster model is critical for \(q \geqslant 1\) ⋮ Unnamed Item ⋮ Comparison and disjoint-occurrence inequalities for random-cluster models. ⋮ Critical probabilities for site and bond percolation models

Cites Work

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• Geometric analysis of \(\phi^ 4\) fields and Ising models. I, II
• On the critical behavior of the magnetization in high-dimensional Ising models
• Contact interactions on a lattice
• Correlation inequalities on some partially ordered sets
• Additive set-valued Markov processes and graphical methods
• Potts models and random-cluster processes with many-body interactions
• Discontinuity of the magnetization in one-dimensional \(1/| x-y| ^ 2\) Ising and Potts models.
• Quantitative Estimates and Rigorous Inequalities for Critical Points of a Graph and Its Subgraphs
• Gibbs States on Countable Sets
• Equality of directional critical exponents in multiparameter percolation models

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