On multiple SLE for the FK–Ising model

Abstract

We prove the convergence of multiple interfaces in the critical planar $\mathit{q}=2$ random cluster model and provide an explicit description of the scaling limit. Remarkably, the expression for the partition function of the resulting multiple ${\mathrm{SLE}}_{16/3}$ 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.