Smirnov's observable for free boundary conditions, interfaces and crossing probabilities

Abstract

We prove convergence results for variants of Smirnov's fermionic observable in the critical Ising model in presence of free boundary conditions. One application of our analysis is a simple proof of a theorem by Hongler and Kytölä on convergence of critical Ising interfaces with plus-minus-free boundary conditions to dipolar SLE(3), and generalization of this result to arbitrary number of arcs carrying plus, minus or free boundary conditions. Another application is a computation of scaling limits of crossing probabilities in FK-Ising model with arbitrary number of alternating wired/free boundary arcs. We also deduce a new crossing formula for the spin Ising model.

27 pages, 2 figures. Several proofs expanded, a small gap fixed in the proof of Theorem 2.6, typos corrected

References in corpus (4)

• Two-Dimensional Critical Percolation: The Full Scaling Limit
• The scaling limits of planar LERW in finitely connected domains
• A solution space for a system of null-state partial differential equations 2
• Virasoro Module Structure of Local Martingales of SLE Variants

Cited by in corpus (1)

• Convergence of the Critical Planar Ising Interfaces to Hypergeometric SLE