Electronic Journal of Probability

Crossing probabilities in topological rectangles for the critical planar FK-Ising model

Dmitry Chelkak, Hugo Duminil-Copin, and Clément Hongler

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We consider the FK-Ising model in two dimensions at criticality. We obtain bounds on crossing probabilities of arbitrary topological rectangles, uniform with respect to the boundary conditions, generalizing results of [DHN11] and [CS12]. Our result relies on new discrete complex analysis techniques, introduced in [Che12].

We detail some applications, in particular the computation of so-called universal exponents, the proof of quasi-multiplicativity properties of arm probabilities, and bounds on crossing probabilities for the classical Ising model.

Article information

Electron. J. Probab. Volume 21, Number (2016), paper no. 5, 28 pp.

Received: 14 April 2014
Accepted: 18 July 2015
First available in Project Euclid: 5 February 2016

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Primary: 60 82

Ising model phase transtion RSW scaling limit FK random-cluster model crossing bounds extremal length

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Chelkak, Dmitry; Duminil-Copin, Hugo; Hongler, Clément. Crossing probabilities in topological rectangles for the critical planar FK-Ising model. Electron. J. Probab. 21 (2016), paper no. 5, 28 pp. doi:10.1214/16-EJP3452. https://projecteuclid.org/euclid.ejp/1454682886

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