A short proof of the discontinuity of phase transition in the planar random-cluster model with $q>4$

Abstract

The goal of this paper is to provide a short proof of the discontinuity of phase transition for the random-cluster model on the square lattice with parameter $q>4$. This result was recently shown via the so-called Bethe ansatz for the six-vertex model. Our proof also exploits the connection to the six-vertex model, but does not rely on the Bethe ansatz. Our argument is soft and only uses very basic properties of the random-cluster model (for example, we do not need the Russo--Seymour--Welsh theory).

arXiv comment13 pages, 4 figures

References in corpus (2)

• The Random-Cluster Model
• Continuity of the phase transition for planar random-cluster and Potts models with $1\le q\le 4$

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