Long Range Ising Models-Phase Transitions and Multiscale Methods

Together with Rodrigo Bissacot

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

  1. Lecture Notes (not available yet)

(Some) Bibliography

For a more complete list, please check the lecture notes and this USP webpage.

Books

  1. S. Friedli and Y. Velenik. Statistical Mechanics of Lattice Systems: A Concrete Mathematical Introduction. Cambridge University Press, (2017).
  2. A. Bovier. Statistical Mechanics of Disordered Systems: A Mathematical Perspective. Cambridge University Press

Articles