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

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.

27 pages, 4 figures

References in corpus (1)

• Convergence of Ising interfaces to Schramm's SLE curves

Cited by in corpus (6)

• Revisiting the combinatorics of the 2D Ising model
• Smirnov's observable for free boundary conditions, interfaces and crossing probabilities
• Conformal invariance of crossing probabilities for the Ising model with free boundary conditions
• Alternating Arm Exponents for the Critical Planar Ising Model
• On the critical parameters of the $q\ge 4$ random-cluster model on isoradial graphs
• Boundary Arm Exponents for SLE$(\kappa )$