The random cluster process

DOI10.1016/0012-365X(94)00120-8zbMath0821.60094OpenAlexW2090760524MaRDI QIDQ1344626

Dominic J. A. Welsh

Publication date: 27 September 1995

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0012-365x(94)00120-8

zbMATH Keywords

reliabilitypercolationIsing modelPotts modelrandom cluster modelelectrical networks

Mathematics Subject Classification ID

Applications of graph theory (05C90) Random graphs (graph-theoretic aspects) (05C80) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Combinatorial probability (60C05) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Cites Work

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• Resistances and currents in infinite electrical networks
• The critical probability of bond percolation on the square lattice equals 1/2
• Correlation inequalities on some partially ordered sets
• Strict inequality for critical values of Potts models and random-cluster processes
• Discontinuity of the magnetization in one-dimensional \(1/| x-y| ^ 2\) Ising and Potts models.
• Bond percolation on honeycomb and triangular lattices
• Percolation Probabilities on the Square Lattice
• Percolation in the random cluster process and Q-state Potts model
• The Computational Complexity of the Tutte Plane: the Bipartite Case
• On the computational complexity of the Jones and Tutte polynomials

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