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On multiple SLE for the FK-Ising model
Konstantin Izyurov · 2020-03-19 · via math.PR updates on arXiv.org

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.

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