Main Page: Difference between revisions
| Line 40: | Line 40: | ||
| Week 2 (27/01) | | Week 2 (27/01) | ||
| | | | ||
* [[T-2|The REM: freezing, condensation, glassiness (Valentina)]] | * [[T-2|The REM: freezing, condensation, glassiness (Valentina)]] <!-- [[Media:2025 P2 solutions.pdf| Sol Prob.2 ]]--> | ||
| | | | ||
* [[L-2| Stochastic Interfaces and growth (Alberto)]] | * [[L-2| Stochastic Interfaces and growth (Alberto)]] | ||
| Line 53: | Line 53: | ||
| Week 4 (10/02) | | Week 4 (10/02) | ||
| | | | ||
* [[T-3| The p-spin model: replicas 1/2, the steps (Valentina)]] [[Media:2025 P3 solutions.pdf| Sol Probs.3 ]] | * [[T-3| The p-spin model: replicas 1/2, the steps (Valentina)]] <!--[[Media:2025 P3 solutions.pdf| Sol Probs.3 ]]--> | ||
| | | | ||
* [[T-4| The p-spin model: replicas 2/2, the interpretation (Valentina)]] [[Media:2025 P4 solutions.pdf| Sol Probs. 4 ]] [[Media:2025_Parisi_scheme.pdf| Notes: Probing states with replicas]] | * [[T-4| The p-spin model: replicas 2/2, the interpretation (Valentina)]] <!--[[Media:2025 P4 solutions.pdf| Sol Probs. 4 ]] [[Media:2025_Parisi_scheme.pdf| Notes: Probing states with replicas]]--> | ||
|-valign=“top" | |-valign=“top" | ||
| Week 5 (17/02) | | Week 5 (17/02) | ||
| Line 65: | Line 65: | ||
| Week 6 (03/03) | | Week 6 (03/03) | ||
| | | | ||
* [[T-5| Rugged landscapes 1/2: counting local minima (Valentina)]] [[Media:2025 P5 solutions.pdf| Sol Prob.5 ]] | * [[T-5| Rugged landscapes 1/2: counting local minima (Valentina)]] <!--[[Media:2025 P5 solutions.pdf| Sol Prob.5 ]]--> | ||
| | | | ||
* [[T-6| Rugged landscapes 2/2: random matrices (Valentina)]] [[Media:2025 P666 solutions .pdf| Sol Prob.6 ]] | * [[T-6| Rugged landscapes 2/2: random matrices (Valentina)]] <!--[[Media:2025 P666 solutions .pdf| Sol Prob.6 ]]--> | ||
|-valign=“top" | |-valign=“top" | ||
| Week 7 (10/03) | | Week 7 (10/03) | ||
| Line 73: | Line 73: | ||
* [[L-7| Anderson localization: introduction (Alberto)]] | * [[L-7| Anderson localization: introduction (Alberto)]] | ||
| | | | ||
* [[T-7| Trap model and aging dynamics (Valentina)]] [[Media:2025 P7 solutions .pdf| Sol Probs.7 ]] | * [[T-7| Trap model and aging dynamics (Valentina)]] <!--[[Media:2025 P7 solutions .pdf| Sol Probs.7 ]]--> | ||
|-valign=“top" | |-valign=“top" | ||
| Week 8 (17/03) | | Week 8 (17/03) | ||
| Line 79: | Line 79: | ||
* [[L-8| Localization in 1D, transfer matrix and Lyapunov exponent (Alberto)]] [[https://colab.research.google.com/drive/1ZJ0yvMrtflWNNmPfaRQ8KTteoWfm0bqk?usp=sharing| notebook]] | * [[L-8| Localization in 1D, transfer matrix and Lyapunov exponent (Alberto)]] [[https://colab.research.google.com/drive/1ZJ0yvMrtflWNNmPfaRQ8KTteoWfm0bqk?usp=sharing| notebook]] | ||
| | | | ||
* [[T-8| Localization on Bethe lattice (1/2): cavity & recursion (Valentina)]] [[Media:2025 P8 solutions.pdf| Sol Prob.8 ]] | * [[T-8| Localization on Bethe lattice (1/2): cavity & recursion (Valentina)]] <!--[[Media:2025 P8 solutions.pdf| Sol Prob.8 ]]--> | ||
|-valign=“top" | |-valign=“top" | ||
| Week 9 (24/03) | | Week 9 (24/03) | ||
| | | | ||
* [[T-9| Localization on Bethe lattice (2/2): stability & mobility edge (Valentina)]] [[Media:2025 P9 solutions.pdf| Sol Prob.9 ]] [[Media:2025_localization_notes.pdf| Notes: Localization: no dissipation, no self-bath]] | * [[T-9| Localization on Bethe lattice (2/2): stability & mobility edge (Valentina)]] <!--[[Media:2025 P9 solutions.pdf| Sol Prob.9 ]] [[Media:2025_localization_notes.pdf| Notes: Localization: no dissipation, no self-bath]]--> | ||
| | | | ||
* [[L-9|Multifractality, tails (Alberto)]] | * [[L-9|Multifractality, tails (Alberto)]] | ||
Latest revision as of 12:48, 4 May 2025
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
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 the Jussieu campus, Room 101, Tours 14 - 24, from 2pm to 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