On multiple SLE for the FK-Ising model
Mathematical Physics
2020-03-20 v1 math.MP
Probability
Abstract
We prove 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 SLE(16/3) 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.
Keywords
Cite
@article{arxiv.2003.08735,
title = {On multiple SLE for the FK-Ising model},
author = {Konstantin Izyurov},
journal= {arXiv preprint arXiv:2003.08735},
year = {2020}
}
Comments
19 pages, 2 figures