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

Yacine Aoun

doi:10.1214/21-ECP390

2021 Sharp asymptotics of correlation functions in the subcritical long-range random-cluster and Potts models

Yacine Aoun

Author Affiliations +

Electron. Commun. Probab. 26: 1-9 (2021). DOI: 10.1214/21-ECP390

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 $\frac{1}{q}\chi {(\beta )^{2}}\beta {J_{0,x}}$ for $\beta \textless {\beta _{c}}$ . The method developed in this article can be applied to any spin model for which there exists a random-cluster representation which is monotonic.

Funding Statement

The author would like to thank the Excellence Fellowship program at the University of Geneva for supporting him during his studies.

Acknowledgments

The author would like to warmly thank Hugo Duminil-Copin for his guidance and help through the master thesis as well as reading and pointing out mistakes in the previous versions of the present article. The author would also like to thank Yvan Velenik, Maëllie Godard and two anonymous referees for many helpful comments.

Citation

Download Citation

Yacine Aoun. "Sharp asymptotics of correlation functions in the subcritical long-range random-cluster and Potts models." Electron. Commun. Probab. 26 1 - 9, 2021. https://doi.org/10.1214/21-ECP390