Sharp asymptotics of correlation functions in the subcritical long-range random-cluster and Potts models

Abstract

For a family of random-cluster models with cluster weights $q\ge 1$, we prove that the probability that $0$ is connected to $x$ is asymptotically equal to $\frac{1}{q}\chi (\beta {)}^2\beta J_{0,x}$. The method developed in this article can be applied to any spin model for which there exists a random-cluster representation which is one-monotonic.

9 pages

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