Probability and Mathematical Physics Seminar

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One-arm exponents of the high-dimensional Ising model

Speaker: Romain Panis, Institut Camille Jordan

Location: Warren Weaver Hall 1302

Date: Friday, May 8, 2026, 11:10 a.m.

Synopsis:

We study the probability that the origin is connected to the boundary of the box of side length n in several percolation models related to the high dimensional Ising model. Our focus is on the random-cluster representation of the Ising model (or FK-Ising model). We prove that different universality classes emerge at criticality depending on the choice of boundary condition. A striking consequence of our results is that the Ising and FK-Ising models exhibit distinct upper critical dimensions, reflecting different underlying mechanisms leading to mean-field behaviour.