A new computation of the critical point for the planar random-cluster model with q≥1

2016/04/13 by Duminil-Copin, Hugo, Raoufi, Aran, Tassion, Vincent
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.1604.03702

Abstract

We present a new computation of the critical value of the random-cluster model with cluster weight q≥ 1 on ℤ². This provides an alternative approach to the result of Beffara and Duminil-Copin. We believe that this approach has several advantages. First, most of the proof can easily be extended to other planar graphs with sufficient symmetries. Furthermore, it invokes RSW-type arguments which are not based on self-duality. And finally, it contains a new way of applying sharp threshold results which avoid the use of symmetric events and periodic boundary conditions.

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