Analyticity of local and global observables in FK-percolation (Loic Gassmann, Université de Fribourg)

05.10.2026 16:15 – 18:00

In most statistical mechanics models, global observables are expected to behave regularly outside of the transition points. In this talk we will investigate this hypothesis in the context of FK-percolation. More precisely, we shall see that under natural mixing and local uniqueness conditions, the probability of local events in FK-percolation are analytic functions of the inverse temperature (except at the transition point). Moreover, an exponential growth bound on the analytic extensions of these probabilities allows to prove the analyticity of several global observables. For instance, our method provides a proof of the analyticity of the magnetisation of the Ising model in any dimension (except at the transition point). The main idea of the proof is to adapt the non-perturbative cluster expansion of Sébastien Ott (arXiv:2003.05879) in order to define a FK-percolation model $\phi^0_{p,q}$ with a complex value of $p$ that extends the real-valued model.

This talk is based on a joint work with Lucas D'Alimonte (arXiv:2604.18558).

Lieu

Bâtiment: Conseil Général 7-9

Room 1-15, Séminaire "Math Physics"

entrée libre