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

Dmitry Chelkak; Hugo Duminil-Copin; Clément Hongler

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arXiv · 1312.7785

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

Dmitry Chelkak·Hugo Duminil-Copin·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 [DCHN11] 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.

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BibTeX RIS

Dmitry Chelkak, Hugo Duminil-Copin, Clément Hongler. 2013-12-30. Crossing probabilities in topological rectangles for the critical planar FK-Ising model. https://arxiv.org/abs/1312.7785

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