Conformal invariance of the planar four-state Potts model and its random-cluster representation

Emile Averous, Hugo Duminil-Copin, Tiancheng He, Piet Lammers, Ioan Manolescu

Source record

Source: arXiv

Published: Oct 6, 2026

arXiv: 2610.08507

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Source abstract

For the critical random-cluster model on $\mathbb Z^2$ with cluster-weight $q=4$ , we prove the convergence of loops to CLE(4) in the scaling limit. Conformal invariance of the four-state Potts model is then deduced via the Edwards-Sokal coupling.

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Conformal invariance of the planar four-state Potts model and its random-cluster representation — Mathematical Frontier Network