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

Probability Seminar

3rd July 2020, 5:30 pm – 6:30 pm

, https://zoom.us/j/93299847543

We give 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 by Duminil-Copin, Gagnebin, Harel, Manolescu and Tassion 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.

Joint work with Gourab Ray

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