Conformal invariance of crossing probabilities for the Ising model with free boundary conditions

Stéphane Benoist, Hugo Duminil-Copin, Clément Hongler

Published 2014-10-14Version 1

We prove that crossing probabilities for the critical planar Ising model with free boundary conditions are conformally invariant in the scaling limit, a phenomenon first investigated numerically by Langlands, Lewis and Saint-Aubin. We do so by establishing the convergence of certain exploration processes towards SLE$(3,\frac{-3}2,\frac{-3}2)$. We also construct an exploration tree for free boundary conditions, analogous to the one introduced by Sheffield.