Main Page

This is the official page for the year 2023-2024 of the Statistical Physics of Disordered Systems course.

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).

• Introduction to disordered systems. The simplest spin-glass: solution of the Random Energy Model.
• The replica method: the solution of the spherical p-spin model (1 RSB). Interface growth.
• Directed polymers in random media: the KPZ universality class.
• Scenarios for the glass transition: sketch of the solution of Sherrington Kirkpatrick model (full RSB); the glass transition in KPZ in 3D.
• Towards glassy dynamics: rugged landscapes, the trap model. Depinning and avalanches.
• Bienaimé-Galton-Watson processes. Anderson localization in 1D.
• Anderson model on the Bethe lattice, and links to the directed polymer problem.
• Quantum thermalization and many-body localization.

Evaluation

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).

Lectures and tutorials

Date	Alberto : 14h00-15h45	Valentina : 16h00-17h45
First Lecture	Spin Glass Transition	Random Energy Model Homework
Second Lecture	Integral Transform: Radon Transform	Interface growth
Third Tutorial	Residue Theorem: Green Functions	Probability: Extreme value Statistics

The Team

• Valentina Ros
• Alberto Rosso

Where and When

• Lectures on Monday: from 2pm to 4 pm
• Tutorials on Monday: from 4 pm to 6pm