COURSE: Phase Transitions in Long-Range Ising Models and Multiscale Methods 

 (January 8 - February 23) (jointly with the Summer Program of IME-USP) 

 with  Lucas Affonso (USP)

Abstract:

Multiscale methods were introduced in the seminal work of Fröhlich and Spencer during the 1980s in the study of phase transitions in statistical mechanics, solving Kac and Thompson conjecture on phase transitions for unidimensional models, to the rigorous proof of the BKT transition and also important results on the study of random Schrodinger operators (later simplified by Klein and Dreifus). Due to its technical difficulty, the use of this method in long-range systems was restricted to unidimensional models after being revisited in many works by Cassandro, Picco, Merola, Pressuti, Rozikov, Ferrari, and many others. This course aims to introduce the students to the recent progress made on the use of the multiscale technique to study phase transitions in multidimensional long-range models. We will also discuss applications in the problem of phase transitions for the random field, nonuniform fields, and cluster expansions.

Content:

Gibbs measures in finite volume. The Ising model. Peierls argument. Imry-Ma argument. Nonuniform (decaying) magnetic fields. The unidimensional long-range Ising model. The multidimensional (short and long)-range Ising model. The Ding-Zhuang strategy on the random field case. Cluster expansions.

Time: 4 pm - 6 pm    Room: Jacy Monteiro Auditorium - ground floor of Bloco B - IME