Mathematical Research Letters

Volume 25 (2018)

Number 3

Configurations of FK Ising interfaces and hypergeometric SLE

Pages: 875 – 889



Antti Kemppainen (Department of Mathematics and Statistics, Faculty of Science, University of Helsinki, Finland)

Stanislav Smirnov (Section de mathématiques, Université de Genève, Switzerland; Skolkovo Institute of Science and Technology, Russia; and Chebyshev Laboratory, St. Petersburg State University, Russia)


In this paper, we show that the interfaces in the FK Ising model at criticality in a domain with $4$ marked boundary points and wired–free–wired–free boundary conditions conditioned on a specific internal arc configuration of interfaces converge in the scaling limit to the hypergeometric SLE (hSLE). The arc configuration consists of a pair of interfaces and the scaling limit of their joint law can be described by an algorithm to sample the pair from an hSLE curve and a chordal SLE (in a random domain defined by the hSLE).

Received 10 April 2017

Accepted 12 September 2017

Published 3 August 2018