Abstract
We prove the convergence of multiple interfaces in the critical planar random cluster model and provide an explicit description of the scaling limit. Remarkably, the expression for the partition function of the resulting multiple 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
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