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

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 (J. Stat. Phys. 98 (2000) 131-244). We do so by establishing the convergence of certain exploration processes towards SLE(3, -3/2, -3/2). We also construct an exploration tree for free boundary conditions, analogous to the one introduced by Sheffield (Duke Math. J. 147 (2009) 79-129).

Published in:
Annales De L Institut Henri Poincare-Probabilites Et Statistiques, 52, 4, 1784-1798
Year:
2016
Publisher:
Cleveland, Inst Mathematical Statistics
ISSN:
0246-0203
Keywords:
Laboratories: