Let G = (V, E) be a finite graph, let Ω be the set Ω = ({0, 1})^E whose members are vectors ω = (ω(e):e element E), and let ℱ be the σ-algebra of all subsets of Ω. A random-cluster model on G is the measure ϕ_(p, q) on the measurable space (Ω, ℱ) defined for each ω by ϕ_(p, q)(ω) = 1/Z( product_(e element E) p^(ω(e)) (1 - p)^(1 - ω(e))) q^(k(ω)) where here, 0<=p<=1 and q>0 are parameters, Z is the so-called partition function Z = sum_(ω element Ω){ product_(e element E) p^(ω(e)) (1 - p)^(1 - ω(e))} q^(k(ω)),

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