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March 2022 On multiple SLE for the FK–Ising model
Konstantin Izyurov
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Ann. Probab. 50(2): 771-790 (March 2022). DOI: 10.1214/21-AOP1547

Abstract

We prove the convergence of multiple interfaces in the critical planar q=2 random cluster model and provide an explicit description of the scaling limit. Remarkably, the expression for the partition function of the resulting multiple SLE16/3 coincides with the bulk spin correlation in the critical Ising model in the half-plane, after formally replacing a position of each spin and its complex conjugate with a pair of points on the real line. As a corollary we recover Belavin–Polyakov–Zamolodchikov equations for the spin correlations.

Acknowledgments

The author is grateful to Alex Karrila, Eveliina Peltola and Hao Wu for stimulating discussions and to the anonymous referee for the suggestions on improving the manuscript.

Citation

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Konstantin Izyurov. "On multiple SLE for the FK–Ising model." Ann. Probab. 50 (2) 771 - 790, March 2022. https://doi.org/10.1214/21-AOP1547

Information

Received: 1 August 2020; Revised: 1 September 2021; Published: March 2022
First available in Project Euclid: 24 March 2022

Digital Object Identifier: 10.1214/21-AOP1547

Subjects:
Primary: 60J67 , 82B20

Keywords: Ising model , random cluster models , Schramm–Lowner evolution

Rights: Copyright © 2022 Institute of Mathematical Statistics

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Vol.50 • No. 2 • March 2022
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