Extract One-arm Exponent in FK Models from the Convergence of Height Functions to GFF

by Jiaming Xia (IHES)

Wednesday Jun 11, 2025, 12:00 PM → 1:00 PM Europe/Paris

Amphithéâtre Léon Motchane (IHES)

Seed Seminar of Mathematics and Physics

We consider FK models with $q$ in $[0,4]$ on the square lattice and the whole plane. We assume the convergence of height functions to GFF and in particular we assume that we know the variance $\sigma^2$ of the GFF. Then, we sketch an approach to get the exponent $\alpha_1$ describing the probability of having a primal crossing of an annulus. The basis for this approach is the BKW coupling relating the height function to the interface loops of FK. We show that by choosing appropriate test functions (viewd as placing charges on the plane), we can get relations between $\sigma^2$, $\alpha_1$, and a factor accounting for local concentration of small interface loops. 

 

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