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

30 Jun 2020  ·  Yacine Aoun ·

For a family of random-cluster models with cluster weights $q\geq 1$, we prove that the probability that $0$ is connected to $x$ is asymptotically equal to $\tfrac{1}{q}\chi(\beta)^{2}\beta J_{0,x}$. 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...

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Probability Mathematical Physics Mathematical Physics 82B20, 82B43 (Primary) 60K35 (Secondary)