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arXiv · 1904.10557

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

Gourab Ray·Yinon Spinka
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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).

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Gourab Ray, Yinon Spinka. 2019-04-23. A short proof of the discontinuity of phase transition in the planar random-cluster model with $q>4$. https://doi.org/10.1007/s00220-020-03827-9

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