Randomness 2024

Workshop at the Institute of Mathematics and Statistics (IME-USP)

5-9 February 2024

The Random Field Ising Model (RFIM) is one of the main examples where the contribution of mathematical physicists was fundamental to a better understanding of a physical model where randomness plays a central role.

This workshop will join experts and young researchers from probability and statistical mechanics working on models such as RFIM and related topics.

Speakers:

Lucas Affonso - University of São Paulo (USP), Brazil
Leandro Chiarini - Durham Unversity, United Kingdom
Christiaan van de Ven - University of Würzburg, Germany
Luiz Renato Fontes - University of São Paulo (USP), Brazil
Christof Külske - Ruhr-Universität Bochum, Germany
João Maia - University of São Paulo (USP), Brazil
Domingos Marchetti - University of São Paulo (USP), Brazil
Pierre Picco - CNRS/Aix-Marseille Université, France
Aldo Procacci - Federal University of Minas Gerais (UFMG), Brazil
Thiago Raszeja - AGH University of Krakow, Poland
Philippe Thieullen - Université de Bordeaux, France
Kelvyn Welsch - University of São Paulo (USP), Brazil

Links for the talks:

05/02

https://youtube.com/live/EjJgegdHYvc?feature=share

https://youtube.com/live/HNMwuY0LIXI?feature=share

06/02

https://youtube.com/live/BiRa6vIMOv4?feature=share

https://youtube.com/live/NRjSxxtZiT4?feature=share

07/02

https://youtube.com/live/JfKrKRNnATE?feature=share

https://youtube.com/live/_NzbpZrB0O4?feature=share

08/02

https://youtube.com/live/ErO7vpAY4Ec?feature=share

09/02

https://youtube.com/live/MolyV0v6FSU?feature=share

COURSE: Phase Transitions in Long-Range Ising Models and Multiscale Methods (January 8 - February 23)

Links for the classes: HERE

(jointly with the Summer Program of IME-USP) - with Lucas Affonso University of São Paulo (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

Some of the main references: