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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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1454682886

Digital Object Identifier
doi:10.1214/16-EJP3452

Subjects
Primary: 60 82

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

Rights
Creative Commons Attribution 4.0 International License.

Citation

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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