We prove convergence results for variants of Smirnov’s fermionic observable in the critical planar Ising model in the 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 a generalization of this result to an arbitrary number of arcs carrying plus, minus or free boundary conditions. Another application is a computation of scaling limits of crossing probabilities in the critical FK-Ising model with an arbitrary number of alternating wired/free boundary arcs. We also deduce a new crossing formula for the spin Ising model.
CITATION STYLE
Izyurov, K. (2015). Smirnov’s Observable for Free Boundary Conditions, Interfaces and Crossing Probabilities. Communications in Mathematical Physics, 337(1), 225–252. https://doi.org/10.1007/s00220-015-2339-3
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