Orateur
Description
Series-Sinai have shown in the nineties that the ferromagnetic n.n. Ising model defined on the Cayley graph of a co-compact group of isometries of the hyperbolic plane $\mathbb{H}_2$ exhibits uncountably many, mutually singular Gibbs states at very low temperature ---one for every bi-infinite geodesic of $\mathbb{H}_2$.
They also conjectured the extremality of their states but the problem has been open ever since.
In this talk I will prove the existence of uncountably many extremal inhomogeneous Gibbs states for the Ising model on regular tilings of $\mathbb{H}_2$. I will also prove a refined Peierls bound for the critical temperature and sketch a few research directions.
Joint work with Loren Coquille (Institut Fourier, Grenoble) and Arnaud Le Ny (LAMA, Université Paris-Est Créteil).
