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 Kyt\"ol\"a 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.
Keywords
Cite
@article{arxiv.1404.0239,
title = {Smirnov's observable for free boundary conditions, interfaces and crossing probabilities},
author = {Konstantin Izyurov},
journal= {arXiv preprint arXiv:1404.0239},
year = {2015}
}
Comments
27 pages, 2 figures. Several proofs expanded, a small gap fixed in the proof of Theorem 2.6, typos corrected