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 and to the sspin glass transition. // The simplest spin-glass: solution of the Random Energy Model.
• Interface growth. // The replica method: the solution of the spherical p-spin model (1/2).
• Directed polymers in random media. // The replica method: the solution of the spherical p-spin model (2/2).
• Scenarios for the glass transition: the glass transition in KPZ in d>2. // Sketch of the solution of Sherrington Kirkpatrick model (full RSB).
• Depinning and avalanches. // Towards glassy dynamics: rugged landscapes.
• Avalanches and Bienaymé-Galton-Watson processes. // Slow dynamics and aging: the trap model.
• Anderson localization: introduction. // The Anderson model on the Bethe lattice: the mobility edge (1/2).
• Localization in 1D: transfer matrix and Lyapunov. // The Anderson model on the Bethe lattice: the mobility edge (2/2).

Lectures and tutorials

Date	Alberto : 14h00-15h45	Valentina : 16h00-17h45
Week 1 (22/01)	Spin Glass Transition	A dictionary. The REM: energy landscape.  Solutions
Week 2 (29/01)	Stochastic Interfaces and growth	The REM: freezing, condensation, glassiness.   Solutions
Week 3 (05/02)	Directed polymer in random media	The p-spin model: replicas (1/2), the steps.  Solutions
Week 4 (12/02)	KPZ and glassiness in finite dimension [notebook]	The p-spin model: replicas (2/2), the interpretation.   Solutions
Week 5 (26/02)	Depinning and avalanches	Rugged landscapes (1/2): counting local minima.   Solutions
Week 6 (04/03)	Bienaymé-Galton-Watson processes	Rugged landscapes (2/2): random matrices. Solutions
Week 7 (11/03)	Anderson localization: introduction	Trap model and aging dynamics. Solutions
Week 8 (18/03)	Localization in 1D, transfer matrix and Lyapunov exponent [notebook]	Anderson localization: the Bethe lattice (1/2). Solutions
Week 9 (25/03)	Multifractality, tails	Anderson localization: the Bethe lattice (2/2). Solutions

Homework

DONE

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, April 8th at ENS, salle Froidevaux (E314) in the geosciences department, staring at 2pm ad ending at 5pm.

Where and When

• Lectures on Monday: from 2pm to 4 pm. Tutorials on Monday: from 4 pm to 6pm.
• Room 14.24.207 in Jussieu campus
• Slack channel for discussions [1]

The Team

• Valentina Ros - vale1925@gmail.com
• Alberto Rosso - alberto.rosso74@gmail.com