Séminaire de Probabilités commun ICJ/UMPA

S-embeddings of the planar Ising model: from crossing estimates to (a glimpse) of Lorentz geometry

by Rémy Mahfouf

Europe/Paris
ENS de Lyon

ENS de Lyon

Salle 435
Description

In this talk we will present the formalism of s-embeddings of weighted abstract planar graphs carrying the Ising model, introduced recently by Chelkak. In that setup and under rather mild geometric assumptions, we derive usual crossing estimates for the FK Ising model that indentifies some critical and near critical regime for a given abstract graph. We finish by presenting new convergence statements enlightening the rather unexpected link between the Ising model and the Lorentz geometry discovered by Chelkak, which leads to reimebed planar graphs as a space-like surface in the Minkowski space.