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Random cluster model

In statistical mechanics, probability theory, graph theory, etc. the random cluster model is a random graph that generalizes and unifies the Ising model, Potts model, and percolation model. It is used to study random combinatorial structures, electrical networks, etc. It is also referred to as the RC model or sometimes the FK representation after its…

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Overview

Definition

Special values of q

Edwards-Sokal representation

Two-dimensional case

History and applications

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Random cluster model

Nodes54
Edges53
Triples22
Avg. degree1.96
Density0.037037
Components1

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Random cluster model

Top relations

related to Edwards-Sokal representation · 11
Random cluster model → Alan, Edwards, ES, It, Let, Potts, Robert, Sokal, The, The Edwards-Sokal, We
related to Special values of q · 5
Random cluster model → Bernoulli, Ising, Potts, The, This
related to Two-dimensional case · 3
Random cluster model → At, If, On
is a · 1
Random cluster model → random graph that generalizes and unifies the Ising model

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Important terminology

displaystyle model cluster random omega graph percolation potts representation bond measure ising configuration open models spin sigma probability rc also

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Random cluster modelis arandom graph that generalizes and unifies the Ising model0.90text
the square latticeinstance ofOn a self-dual graph0.80text
a phase transition can only occur at the self-dual coupling v self-dualinstance ofOn a self-dual graph0.80text
Random cluster modelrelated to Edwards-Sokal representationThe Edwards-Sokal0.60section
Random cluster modelrelated to Edwards-Sokal representationES0.60section
Random cluster modelrelated to Edwards-Sokal representationPotts0.60section
Random cluster modelrelated to Edwards-Sokal representationRobert0.60section
Random cluster modelrelated to Edwards-Sokal representationEdwards0.60section
Random cluster modelrelated to Edwards-Sokal representationAlan0.60section
Random cluster modelrelated to Edwards-Sokal representationSokal0.60section
Random cluster modelrelated to Edwards-Sokal representationIt0.60section
Random cluster modelrelated to Edwards-Sokal representationLet0.60section

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