Objective
To introduce the students to multiscale techniques applied to statiscal mechanics with focus on the long-range Ising models in the
lattice.
Information
This course will be given during the Summer of 2024 at IME-USP. This will also be part of the Conference Randomness 2024.
The classes will be from Monday to Thursday, starting 16:00 until 18:00, local time.
See also the USP webpage for this course.
Content
Gibbs measures in finite volume. The Ising model. Peierls argument. Imry-Ma argument. Nonuniform magnetic field.
The unidimensional long-range Ising model. The multidimensional Ising model. The Ding-Zhuang strategy on the random field case.
Cluster expansions.
Material
- Lecture Notes (not available yet)
(Some) Bibliography
For a more complete list, please check the lecture notes and this USP webpage.
Books
- S. Friedli and Y. Velenik. Statistical Mechanics of Lattice Systems: A Concrete Mathematical Introduction. Cambridge University Press, (2017).
- A. Bovier. Statistical Mechanics of Disordered Systems: A Mathematical Perspective. Cambridge University Press
Articles