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arXiv · 2007.00116

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

Yacine Aoun
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Abstract

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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Yacine Aoun. 2020-06-30. Sharp asymptotics of correlation functions in the subcritical long-range random-cluster and Potts models. https://doi.org/10.1214/21-ecp390

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