Extremal Ising Gibbs States on hyperbolic lattices

par Loren Coquille

jeudi 27 nov. 2025, 14:00 → 15:00 Europe/Paris

Fokko du Cloux (ICJ)

I will explain how to exhibit an uncountable family of extremal (non-automorphism invariant) Gibbs measures of the low temperature Ising model on regular tilings of the hyperbolic plane. These states arise as low temperature perturbations of local ground states having a sparse enough set of frustrated edges, the sparseness being measured in terms of the isoperimetric constant of the graph.

Deducing extremality of Series-Sinai states (having one interface along a continuous geodesic of H^2) amounts to answer a nice question about hyperbolic billiards.

 

Based on a joint work with Matteo D’Achille and Arnaud Le Ny.