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


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).
* 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 until 16th February
* Room 209 in Jussieu campus, Tours 56-66 209 from 2nd March  '''Attention: ROOM CHANGE!'''
* Each session is a mixture of lectures and exercises.


= The Team =


*  Introduction to disordered systems. The simplest spin-glass: solution of the Random Energy Model.
*  [https://vale1925.wixsite.com/vros Valentina Ros] - vale1925@gmail.com
*  Interface growth. The replica method: the solution of the spherical p-spin model (1/2).
* [http://lptms.u-psud.fr/alberto_rosso/ Alberto Rosso] - alberto.rosso74@gmail.com
* Directed polymers in random media: the KPZ universality class. The replica method: the solution of the spherical p-spin model (2/2).
* Scenarios for the glass transition: sketch of the solution of Sherrington Kirkpatrick model (full RSB); the glass transition in KPZ in d>2.
*  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 ==
= Course description =


The students have two possibilities:
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.


(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).
'''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=
=Lectures and tutorials=
'''If the layout of the formulas is bad, it might be because you are using Safari. Try opening the wiki with Firefox or Chrome.'''


{| class="wikitable" border="1"
{| class="wikitable" border="1"
|-
|-
! width="100"|Date
! width="100"|Date
! width="500"|  Alberto : 14h00-15h45
! width="500"|  14h00-15h45
! width="500"| Valentina : 16h00-17h45
! width="500"| 16h00-17h45


|-valign="top"
|-valign="top"


| First Week
| Week 1 (19/01)
|
|
* [[L-1| Spin Glass Transition]]
* [[L1_ICTS| Spin Glass Transition (Alberto)]]
<!--[[H_1|Exercises on Extreme Values Statistics]]-->
|   
|   
* [[T-I|  Random Energy Model: freezing transition]]
* [[T-I|  A dictionary. The REM: energy landscape (Valentina)]]&nbsp; [[Media:2025 P1 solutions.pdf| Sol Prob.1 ]]
  [[ST-I| Solutions]]
  |-valign=“top"


|-valign="top"
|-valign=“top"
| Second Week
| Week 2 (26/01)
|
* [[L2_ICFP| Stochastic Interfaces and growth (Alberto)]]
|
|
* [[L-2|Stochastic Interfaces and growth]]
* [[T-2|The REM: freezing, condensation, glassiness (Valentina)]] &nbsp; [[Media:2025 P2 solutions.pdf| Sol Prob.2 ]]
 
|-valign=“top"
|  
* [[T-2| p-spin model: the replica method (1/2)]]
  [[ST-2| Solutions]]


|-valign=“top"
|-valign=“top"
| Third Week
| Week 3 (02/02)
|
|
* [[L-3|Directed polymer in random media]]
* [[L-3|Directed polymer in random media (Alberto)]]
 
|   
|   
* [[T-3| p-spin model: the replica method (2/2)]]
* [[L-4| KPZ and glassiness in finite dimension (Alberto)]] [[https://colab.research.google.com/drive/1PTya42ZS2kU87A-BxQFFIUDTs_k47men?usp=sharing| notebook]]
  [[ST-3| Solutions]]
 
|-valign=“top"
|-valign=“top"
| Fourth Week
| Week 4 (9/02) and Week 5 (16/02)
|
|
* [[L-4| KPZ and glassiness in finite dimension]]
* [[T-3| Spin glasses, equilibrium: replicas, the steps (Valentina)]]&nbsp;  [[Media:2025 P3 solutions.pdf| Sol Prob.3 ]]
|   
|   
* [[T-4| On low-T phase of mean-field glasses]]
* [[T-4| Spin glasses, equilibrium: replicas, the interpretation (Valentina)]] &nbsp;  [[Media:2025 P4 solutions.pdf| Sol Probs. 4 ]]&nbsp;
  [[ST-4| Solutions]]
[[Media:2025_Parisi_scheme.pdf| Notes: Probing states with replicas]]
|-valign=“top"
|-valign=“top"
| Fifth Week
| Week 6 (02/03)
|
|
* [[L-5| xxx]]
* [[LBan-IV| Driven Disordered Materials  (Alberto)]] [[Media:DISSYTS.pdf| Slides ]]
|   
|   
* [[T-5| Rugged Landscapes: Kac-Rice method]]
* [[LBan-V| Avalanches in Disordered Materials (Alberto)]]
  [[ST-5| Solutions]]
|-valign=“top"


| Week 7 (9/03)
|
* [[L-7| Anderson localization: introduction (Alberto)]]
|
* [[T-5| Rugged landscapes: counting metastable states (Valentina)]] &nbsp;[[Media:2025 P5 solutions.pdf| Sol Prob.5 ]]
|-valign=“top"
|-valign=“top"
| Sixth Week
| Week 8 (16/03)
|
|
* [[L-6| xxx]]
* [[T-6| Rugged landscapes: stability of metastable states (Valentina)]] <!--[[Media:2025 P666 solutions .pdf| Sol Prob.6 ]]-->
| 
* [[T-6| XXXX]]
|-valign=“top"
|  Seventh Week
|
|
* [[L-7| xxx]]
* [[T-7| Trap model and aging dynamics (Valentina)]] <!--[[Media:2025 P7 solutions .pdf| Sol Probs.7 ]]-->
| 
* [[T-7| XXXX]]
|-valign=“top"
|-valign=“top"
| Eight Week
| Week 9 (23/03)
|
|
* [[L-8| xxx]]
* [[L-8| Localization in 1D, transfer matrix and Lyapunov exponent (Alberto)]]  [[https://colab.research.google.com/drive/1ZJ0yvMrtflWNNmPfaRQ8KTteoWfm0bqk?usp=sharing| notebook]]
|   
|   
* [[T-8| XXXX]]
* [[L-9|Multifractality, tails (Alberto)]]
|-valign=“top"
|-valign=“top"
| Nineth Week
| Extra
|
|
* [[L-9| xxx]]
* [[T-8| Localization on Bethe lattice: cavity & recursion (Valentina)]] <!--[[Media:2025 P8 solutions.pdf| Sol Prob.8 ]]-->
|   
|   
* [[T-9| XXXX]]
* [[T-9| Localization on Bethe lattice: stability & mobility edge (Valentina)]] <!--[[Media:2025 P9 solutions.pdf| Sol Prob.9 ]]&nbsp;
[[Media:2025_localization_notes.pdf| Notes: Localization: no dissipation, no self-bath]]-->
|}
|}


== Homework ==
<!--== Homework ==
There are two homeworks: Homework 1 on Random Matrices, and Homework 2 on the topics of the lecture.
[[Media:RMT_introduction.pdf| Homework 1 on Random Matrices ]]
[[Media:2025_HW2.pdf| 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: [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]-->
 
= Exercises =
 
 
<li> Week 1: [[Media:Exercises_1-3.pdf| Exercises 1-3 on extreme value statistics]]
</li>
 
<li> Week 2:
[[Media:Tutorial_and_Exercise_4.pdf| Tutorial and Exercise 4 on random matrices]] <br>
[[Media:Exercises_5-6.pdf| Exercises 5-6 on the random energy model]]
</li>
 
<li> Week 3:
[[Media:Exercises 7&8.pdf| Exercises 7-8 on interfaces]]
</li>
 
<li> Week 4:
[[Media:Exercises 9-10.pdf| Exercises 9-10 on glassiness]]
</li>
 
<li> Week 5 and 6:
[[Media:11-12_Exercises.pdf| Exercises 11-12 on dynamics]]
</li>
 
<li> Week 7:
[[Media:Exercises_13_15.pdf| Exercises 13-15 on branching and localization]]
</li>


[[Homework | Homework]]
<li> Week 8:
[[XX| Exercises 16-17 on trap model and localization]]
</li>


== The Team ==
<li>
[[Media:DISSYTS.pdf| Slides ]]
</li>


*  [https://vale1925.wixsite.com/vros  Valentina Ros]
= Evaluation and exam =
* [http://lptms.u-psud.fr/alberto_rosso/ Alberto Rosso]


The exam will be on '''Monday, March 30th 2026'''. It will be written, 3h long. It consists of two parts:


== Where and When ==
Part 1: theory questions, see here for an example.


* Lectures on Monday: from 2pm to 4 pm
Part 2: you will be asked to solve pieces of the 17 exercises given to you in advance.
* Tutorials on Monday:  from 4 pm to 6pm
 
'''You are not allowed to bring any material (printed notes, handwritten notes) nor to use any device during the exam.'''
 
All relevant formulas will be provided in the text of the exam. There will be one  printed version of the WIKI pages available to you to consult.
 
 
<!--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.'''-->

Latest revision as of 11:36, 11 March 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 until 16th February
  • Room 209 in Jussieu campus, Tours 56-66 209 from 2nd March Attention: ROOM CHANGE!
  • Each session is a mixture of lectures and exercises.

The Team

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

If the layout of the formulas is bad, it might be because you are using Safari. Try opening the wiki with Firefox or Chrome.

Date 14h00-15h45 16h00-17h45
Week 1 (19/01)
Week 2 (26/01)
Week 3 (02/02)
Week 4 (9/02) and Week 5 (16/02)

Notes: Probing states with replicas

Week 6 (02/03)
Week 7 (9/03)
Week 8 (16/03)
Week 9 (23/03)
Extra


Exercises

  • Week 1: Exercises 1-3 on extreme value statistics
  • Week 2: Tutorial and Exercise 4 on random matrices
    Exercises 5-6 on the random energy model
  • Week 3: Exercises 7-8 on interfaces
  • Week 4: Exercises 9-10 on glassiness
  • Week 5 and 6: Exercises 11-12 on dynamics
  • Week 7: Exercises 13-15 on branching and localization
  • Week 8: Exercises 16-17 on trap model and localization
  • Slides

    • Evaluation and exam

    The exam will be on Monday, March 30th 2026. It will be written, 3h long. It consists of two parts:

    Part 1: theory questions, see here for an example.

    Part 2: you will be asked to solve pieces of the 17 exercises given to you in advance.

    You are not allowed to bring any material (printed notes, handwritten notes) nor to use any device during the exam.

    All relevant formulas will be provided in the text of the exam. There will be one printed version of the WIKI pages available to you to consult.


    Retrieved from "http://www.lptms.universite-paris-saclay.fr//wikids/index.php?title=Main_Page&oldid=4235"