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arXiv · 2610.08507

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
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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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Emile Averous, Hugo Duminil-Copin, Tiancheng He, Piet Lammers, Ioan Manolescu. 2026-10-06. Conformal invariance of the planar four-state Potts model and its random-cluster representation. https://arxiv.org/abs/2610.08507

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