Fortuin–Kasteleyn random cluster model
E906308
The Fortuin–Kasteleyn random cluster model is a unifying probabilistic framework in statistical mechanics that represents spin systems and percolation models, notably providing a graphical reformulation of the Potts model.
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
lattice model in statistical mechanics
ⓘ
percolation-type model ⓘ probabilistic model ⓘ |
| alsoKnownAs |
FK random cluster model
NERFINISHED
ⓘ
random cluster model ⓘ |
| associatedWith | FKG inequality NERFINISHED ⓘ |
| basedOn | configurations of open and closed edges on a graph ⓘ |
| connectedTo |
Gibbs measures
NERFINISHED
ⓘ
graph theory ⓘ percolation clusters ⓘ |
| definedOn |
finite graphs
ⓘ
lattices such as Z^d ⓘ |
| field |
mathematical physics
ⓘ
probability theory ⓘ statistical mechanics ⓘ |
| frameworkFor | unified treatment of spin and percolation models ⓘ |
| generalizes | Bernoulli bond percolation ⓘ |
| hasApplication | Monte Carlo algorithms for Potts and Ising models ⓘ |
| hasContinuumLimitRelatedTo | Schramm–Loewner evolution in two dimensions GENERATED ⓘ |
| hasParameter |
cluster weight q
ⓘ
edge occupation probability p ⓘ |
| hasProperty | positively associated for q ≥ 1 ⓘ |
| hasVariant |
free boundary conditions
ⓘ
wired boundary conditions ⓘ |
| importantFor | conformal invariance studies in 2D ⓘ |
| inspired | cluster algorithms such as Swendsen–Wang ⓘ |
| introducedInContextOf | graphical representations of spin systems ⓘ |
| namedAfter |
Cornelis M. Fortuin
NERFINISHED
ⓘ
Pieter W. Kasteleyn NERFINISHED ⓘ |
| probabilityWeightProportionalTo |
(1-p)^{number of closed edges}
ⓘ
p^{number of open edges} ⓘ q^{number of connected components} ⓘ |
| provides | graphical reformulation of the Potts model ⓘ |
| reducesTo | Bernoulli bond percolation when q = 1 ⓘ |
| relatedTo |
Ising model as the q = 2 case
ⓘ
q-state Potts model NERFINISHED ⓘ |
| studiedFor |
correlation inequalities
ⓘ
critical phenomena ⓘ phase transitions ⓘ |
| unifies |
Ising model
NERFINISHED
ⓘ
Potts model NERFINISHED ⓘ percolation theory ⓘ |
| usedIn |
rigorous study of Potts model phase diagram
ⓘ
study of percolation of FK clusters ⓘ |
| usedToConstruct | random-cluster measures on infinite graphs ⓘ |
| uses | cluster representation of spin systems ⓘ |
Referenced by (1)
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