Main Page
Welcome to the WIKI page of the M2 ICFP course on the Statistical Physics of Disordered Systems, second semester 2025.
Course description
This course deals with systems in which the presence of impurities or amorphous structures (in other words, of disorder) influences radically the physics, generating novel phenomena. These phenomena involve the properties of the system at equilibrium (freezing and glass transitions), as well as their dynamical evolution out-of-equilibrium (pinning, avalanches), giving rise to ergodicity breaking both in absence and in presence of quantum fluctuations (classical metastability, quantum localization). We discuss the main statistical physics models that are able to capture the phenomenology of these systems, as well as the powerful theoretical tools (replica theory, large deviations, random matrix theory, scaling arguments, strong-disorder expansions) that have been developed to characterize quantitatively their physics. These theoretical tools nowadays have a huge impact in a variety of fields that go well-beyond statistical physics (computer science, probability, condensed matter, theoretical biology). Below is a list of topics discussed during the course.
Finite-dimensional disordered systems:
- Introduction to disordered systems and to the spin glass transition.
- Interface growth. Directed polymers in random media. Scenarios for the glass transition: the glass transition in KPZ in d>2.
- Depinning and avalanches. Bienaymé-Galton-Watson processes.
- Anderson localization: introduction. Localization in 1D: transfer matrix and Lyapunov.
Mean-field disordered systems:
- The simplest spin-glass: solution of the Random Energy Model.
- The replica method: the solution of the spherical p-spin model. Sketch of the solution of Sherrington Kirkpatrick model (full RSB).
- Towards glassy dynamics: rugged landscapes. Slow dynamics and aging: the trap model.
- The Anderson model on the Bethe lattice: the mobility edge.
Lectures and tutorials
| Date | 14h00-15h45 | 16h00-17h45 |
|---|---|---|
| Week 1 (20/01) | ||
| Week 2 (27/01) | ||
| Week 3 (03/02) | ||
| Week 4 (10/02) | ||
| Week 5 (17/02) | ||
| Week 6 (03/03) | ||
| Week 7 (10/03) | ||
| Week 8 (17/03) | ||
| Week 9 (24/03) |
Homework (updated!)
There are two homeworks: Homework 1 on Random Matrices, and Homework 2 on the topics of the lecture.
Homework 2 on topics of lectures
Homework 1 is worth 5 points, Homework 2 is worth 15 points.
In the final grade calculation, the total score from both assignments will have a weight of 0.25, while the exam will account for 0.75.
Homework 1 due by Monday, February 17th.
Homework 2 due by Monday, March 24th.
Extra
Here is a notebook on random matrices (made by M. Biroli) with two coding exercises. You can download the notebook from the link below, and use the online platform: Jupyter to modify the notebook and add the solutions to the two exercises.
Homework 1: notebook
Practical Information
Evaluation and exam
The students have two possibilities:
(1) A final written exam which counts for the total grade.
(2) An homework assignement + a written exam. The final grade is given by a weighted average of the two grades (the homework counts 1/4 and the written exam 3/4).
The written exam will be on Monday, March 31st 2025 in TBA, staring at 2pm ad ending at 5pm.
Where and When
- Course on Monday, from 2pm to 6 pm. Each session is a mixture of lectures and exercises.
- Room 107 in Jussieu campus, Tours 23-24
The Team
- Valentina Ros - vale1925@gmail.com
- Alberto Rosso - alberto.rosso74@gmail.com