Percolation and ferromagnetism on \(\mathbb Z^ 2\): the \(q\)-state Potts cases

DOI10.1016/S0304-4149(96)00106-8zbMath0889.60096OpenAlexW2151200071MaRDI QIDQ1382482

Lincoln Chayes

Publication date: 29 March 1998

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0304-4149(96)00106-8

zbMATH Keywords

percolationPotts modelFKG inequalities

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Phase transitions (general) in equilibrium statistical mechanics (82B26) Percolation (82B43)

Related Items (6)

Representation and poly-time approximation for pressure of \(\mathbb Z^2\) lattice models in the non-uniqueness region ⋮ Sharp thresholds for the random-cluster and Ising models ⋮ A note on disagreement percolation ⋮ Percolation phenomena in low and high density systems ⋮ Random cluster models on the triangular lattice ⋮ Positive correlations in the fuzzy Potts model

Cites Work

• Unnamed Item
• Interfaces in the Potts model. I: Pirogov-Sinai theory of the Fortuin- Kasteleyn representation
• An upper bound on the critical percolation probability for the three- dimensional cubic lattice
• On the uniqueness of the infinite occupied cluster in dependent two- dimensional site percolation
• Agreement percolation and phase coexistence in some Gibbs systems.
• Potts models and random-cluster processes with many-body interactions
• Precolation of the minority spins in high-dimensional Ising models
• The stochastic random-cluster process and the uniqueness of random-cluster measures
• Discontinuity of the magnetization in one-dimensional \(1/| x-y| ^ 2\) Ising and Potts models.

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