A Short Proof of the Discontinuity of Phase Transition in the Planar Random-Cluster Model with q> 4

Gourab Ray, Yinon Spinka

Research output: Contribution to journalArticlepeer-review

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 in Duminil-Copin et al. (arXiv:1611.09877, 2016) 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 (in particular, it does not rely on a computation of the correlation length) and only uses very basic properties of the random-cluster model [for example, we do not even need the Russo–Seymour–Welsh machinery developed recently in Duminil-Copin et al. (Commun Math Phys 349(1):47–107, 2017)].

Original languageEnglish
Pages (from-to)1977-1988
Number of pages12
JournalCommunications in Mathematical Physics
Volume378
Issue number3
DOIs
StatePublished - 1 Sep 2020
Externally publishedYes

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