Seminars: S. B. Shlosman, The Ising model and the Airy diffusion

SEMINARS


Globus Seminar April 14, 2016 15:40, Moscow, IUM (Bolshoi Vlas'evskii per., 11)

The Ising model and the Airy diffusion S. B. Shlosman^ab ^a CNRS – Center of Theoretical Physics ^b Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
Abstract: I will talk about the Ising model — the drosophila of the rigorous statistical physics. It turns out that some new phenomena which appear in modern mathematical physics, can be observed in the Ising model as well. One example which I will focus on is the size of typical fluctuations of the extended systems. If the size of the system is $N$, then the usual (gaussian) fluctuations are of the order of $N^{1/2}$. While in the random matrix theory one sees the fluctuations of the order $N^{1/3}$. I will explain that one can see them in the Ising model as well — one just needs to know where to look. Namely, the level lines of the Ising droplet near its edge have fluctuations of the desired order. When scaled by $N^{1/3}$, their limiting behavior for large $N$ is given by the Airy diffusion process. Joint work with D. Ioffe and Y. Velenik. The talk will be held in Russian.