English

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

R2 v1 2026-06-23T14:20:01.442Z