A new computation of the critical point for the planar random-cluster model with $q\ge1$

Hugo Duminil-Copin; Aran Raoufi; Vincent Tassion

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arXiv · 1604.03702

A new computation of the critical point for the planar random-cluster model with $q\ge1$

Hugo Duminil-Copin·Aran Raoufi·Vincent Tassion

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Abstract

We present a new computation of the critical value of the random-cluster model with cluster weight $q\ge 1$ on $\mathbb{Z}^2$. 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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BibTeX RIS

Hugo Duminil-Copin, Aran Raoufi, Vincent Tassion. 2016-04-13. A new computation of the critical point for the planar random-cluster model with $q\ge1$. https://arxiv.org/abs/1604.03702

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