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Welcome to the WIKI page of the M2 ICFP course on the Statistical Physics of Disordered Systems, second semester | Welcome to the WIKI page of the M2 ICFP course on the Statistical Physics of Disordered Systems, second semester 2026. | ||
== Course description | = Where and When = | ||
* Each Monday at 2pm - 6 pm, from January 19th to March 23rd. No lecture on 23/02/26. | |||
* Room 202 in Jussieu campus, Tours 54-55. | |||
* Each session is a mixture of lectures and exercises. | |||
= The Team = | |||
* [https://vale1925.wixsite.com/vros Valentina Ros] - vale1925@gmail.com | |||
* [http://lptms.u-psud.fr/alberto_rosso/ Alberto Rosso] - alberto.rosso74@gmail.com | |||
= 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. | 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. | ||
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| Week 1 ( | | Week 1 (19/01) | ||
| | | | ||
* [[ | * [[L1_ICTS| Spin Glass Transition (Alberto)]] | ||
[[H_1|Exercises on Extreme Values Statistics]] | |||
| | | | ||
* [[T-I| A dictionary. The REM: energy landscape (Valentina)]] [[Media:2025 P1 solutions.pdf| Sol Prob.1 ]] | * [[T-I| A dictionary. The REM: energy landscape (Valentina)]] <!--[[Media:2025 P1 solutions.pdf| Sol Prob.1 ]]--> | ||
|-valign=“top" | |-valign=“top" | ||
| Week 2 ( | | Week 2 (26/01) | ||
| | | | ||
* [[T-2|The REM: freezing, condensation, glassiness (Valentina)]] [[Media:2025 P2 solutions.pdf| Sol Prob.2 ]] | * [[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)]] | ||
|-valign=“top" | |-valign=“top" | ||
| Week 3 ( | | Week 3 (02/02) | ||
| | | | ||
* [[L-3|Directed polymer in random media (Alberto)]] | * [[L-3|Directed polymer in random media (Alberto)]] | ||
| Line 51: | Line 63: | ||
* [[L-4| KPZ and glassiness in finite dimension (Alberto)]] [[https://colab.research.google.com/drive/1PTya42ZS2kU87A-BxQFFIUDTs_k47men?usp=sharing| notebook]] | * [[L-4| KPZ and glassiness in finite dimension (Alberto)]] [[https://colab.research.google.com/drive/1PTya42ZS2kU87A-BxQFFIUDTs_k47men?usp=sharing| notebook]] | ||
|-valign=“top" | |-valign=“top" | ||
| Week 4 ( | | Week 4 (9/02) | ||
| | | | ||
* [[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 ]] | * [[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 ( | | Week 5 (16/02) | ||
| | | | ||
* [[L-5| Depinning and avalanches (Alberto)]] | * [[L-5| Depinning and avalanches (Alberto)]] | ||
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* [[L-6| Bienaymé-Galton-Watson processes (Alberto)]] | * [[L-6| Bienaymé-Galton-Watson processes (Alberto)]] | ||
|-valign=“top" | |-valign=“top" | ||
| Week 6 ( | | Week 6 (02/03) | ||
| | | | ||
* [[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 ( | | Week 7 (9/03) | ||
| | | | ||
* [[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= | |-valign=“t0p" | ||
| Week 8 ( | | Week 8 (16/03) | ||
| | | | ||
* [[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| | * [[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 ( | | Week 9 (23/03) | ||
| | | | ||
* [[T-9| | * [[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)]] | ||
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== Homework | <!--== Homework == | ||
There are two homeworks: Homework 1 on Random Matrices, and Homework 2 on the topics of the lecture. | There are two homeworks: Homework 1 on Random Matrices, and Homework 2 on the topics of the lecture. | ||
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'''Extra''' | '''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: [https://jupyter.org/try-jupyter/lab/ Jupyter] to modify the notebook and add the solutions to the two exercises. | 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: [https://jupyter.org/try-jupyter/lab/ Jupyter] to modify the notebook and add the solutions to the two exercises. | ||
[https://colab.research.google.com/drive/13z_RnRlCq5p3ihDQulOPftqb05nsrTqQ?usp=sharing| Homework 1: notebook] | [https://colab.research.google.com/drive/13z_RnRlCq5p3ihDQulOPftqb05nsrTqQ?usp=sharing| Homework 1: notebook]--> | ||
= | = Evaluation and exam = | ||
The students have two possibilities: | |||
<!--The students have two possibilities: | |||
(1) A final written exam which counts for the total grade. | (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). | (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.'''--> | |||
'''The written exam will be on Monday, March 31st 2025 in | |||
Latest revision as of 14:57, 18 January 2026
Welcome to the WIKI page of the M2 ICFP course on the Statistical Physics of Disordered Systems, second semester 2026.
Where and When
- Each Monday at 2pm - 6 pm, from January 19th to March 23rd. No lecture on 23/02/26.
- Room 202 in Jussieu campus, Tours 54-55.
- Each session is a mixture of lectures and exercises.
The Team
- Valentina Ros - vale1925@gmail.com
- Alberto Rosso - alberto.rosso74@gmail.com
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 (19/01) | ||
| Week 2 (26/01) | ||
| Week 3 (02/02) | ||
| Week 4 (9/02) | ||
| Week 5 (16/02) | ||
| Week 6 (02/03) | ||
| Week 7 (9/03) | ||
| Week 8 (16/03) | ||
| Week 9 (23/03) |