Metastability of Ising/Potts models in large volumes in the zero-temperature limit

11.08.2022 14:00 - 16:00

Seonwoo Kim (Seoul National University)

Abstract: In this talk, we consider Ising/Potts models on finite 2D Euclidean lattices in the zero-temperature limit, which are classical spin systems studied from the early 20th century. In the case where the lattice is fixed, there are a lot of references starting from the fundamental work [Neves and Schonmann, CMP 1991]. However, in the case where the lattice size also diverges, the results are much more limited.
We introduce our recent research on this large-volume model under zero external field. There is an interesting phenomenon of phase transition triggered by a competition between rates of divergence to infinity of the inverse temperature and the lattice size. Moreover, in the regime where the inverse temperature diverges sufficiently faster than the lattice size, we formulate the metastable behavior using the Eyring-Kramers formula and the Markov chain model reduction method. Our approach is universal in the sense that similar results can be obtained for any types of lattice structures given to the two-dimensional plane. This talk is based on a joint work with Insuk Seo.

A. Glazman

BZ 2, 2. OG., OMP 1