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Welcome to the WIKI page for the year 2024-2025 of the ICFP course on Statistical Physics of Disordered Systems.

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)	Spin Glass Transition (Alberto)	A dictionary. The REM: energy landscape (Valentina)
Week 2 (27/01)	The REM: freezing, condensation, glassiness (Valentina)	Stochastic Interfaces and growth (Alberto)
Week 3 (03/02)	Directed polymer in random media (Alberto)	KPZ and glassiness in finite dimension (Alberto) [notebook]
Week 4 (10/02)	The p-spin model: replicas (1/2), the steps (Valentina)	The p-spin model: replicas (2/2), the interpretation (Valentina)
Week 5 (17/02)	Depinning and avalanches (Alberto)	Bienaymé-Galton-Watson processes (Alberto)
Week 6 (03/03)	Rugged landscapes (1/2): counting local minima (Valentina)	Rugged landscapes (2/2): random matrices (Valentina)
Week 7 (10/03)	Anderson localization: introduction (Alberto)	Trap model and aging dynamics (Valentina)
Week 8 (17/03)	Localization in 1D, transfer matrix and Lyapunov exponent (Alberto) [notebook]	Anderson localization (1/2): the Bethe lattice (Valentina)
Week 9 (24/03)	Multifractality, tails (Alberto)	Anderson localization (2/2): the Bethe lattice (Valentina)

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, 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 TBA in Jussieu campus
• Slack channel for discussions [1]

The Team

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