One-arm exponents of the high-dimensional Ising model
Date(s) : 07/04/2026 iCal
14h30 - 15h30
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.
Emplacement
I2M Saint-Charles - Salle de séminaire
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