Configurations of FK Ising interfaces and hypergeometric SLE

2017/04/10 by Antti Kemppainen, Stanislav Smirnov, Kemppainen, Antti +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #math-ph #math.MP #math.PR

paper · pdf · doi:10.48550/arxiv.1704.02823

8 pages, 2 figures

arxiv created 2017/04/10 · arxiv updated 2017/04/11

Abstract

In this paper, we show that the interfaces in FK Ising model in any 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 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 a hSLE curve and a chordal SLE (in a random domain defined by the hSLE).

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• Ising Interfaces and Free Boundary Conditions
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