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= Where and When =
= Where and When =


* Course on Monday, from 2pm to 6 pm. Each session is a mixture of lectures and exercises.  
* 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
* 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 =
= The Team =
Line 32: Line 34:


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


| Week 1 (20/01)
| Week 1 (19/01)
|
|
* [[L-1| Spin Glass Transition (Alberto)]]
* [[L1_ICTS| Spin Glass Transition (Alberto)]]
<!--[[H_1|Exercises on Extreme Values Statistics]]-->
|   
|   
* [[T-I|  A dictionary. The REM: energy landscape (Valentina)]]&nbsp; <!--[[Media:2025 P1 solutions.pdf| Sol Prob.1 ]]-->
* [[T-I|  A dictionary. The REM: energy landscape (Valentina)]]&nbsp; [[Media:2025 P1 solutions.pdf| Sol Prob.1 ]]
   |-valign=“top"
   |-valign=“top"


| Week 2 (27/01)
|-valign=“top"
| Week 2 (26/01)
|
|
* [[T-2|The REM: freezing, condensation, glassiness (Valentina)]] &nbsp;  <!--[[Media:2025 P2 solutions.pdf| Sol Prob.2 ]]-->
* [[L2_ICFP| Stochastic Interfaces and growth (Alberto)]]
|
|
* [[L-2| Stochastic Interfaces and growth (Alberto)]]
* [[T-2|The REM: freezing, condensation, glassiness (Valentina)]] &nbsp;  [[Media:2025 P2 solutions.pdf| Sol Prob.2 ]]
|-valign=“top"


|-valign=“top"
|-valign=“top"
| Week 3 (03/02)
| Week 3 (02/02)
|
|
* [[L-3|Directed polymer in random media (Alberto)]]
* [[L-3|Directed polymer in random media (Alberto)]]
Line 61: Line 69:
* [[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 (10/02)
| Week 4 (9/02)
|
|
* [[T-3| The p-spin model: replicas 1/2, the steps (Valentina)]]&nbsp;  <!--[[Media:2025 P3 solutions.pdf| Sol Probs.3 ]]-->
* [[T-3| Spin glasses, equilibrium: replicas, the steps (Valentina)]]&nbsp;  [[Media:2025 P3 solutions.pdf| Sol Prob.3 ]]
|   
|   
* [[T-4| The p-spin model: replicas 2/2, the interpretation (Valentina)]] &nbsp;  <!--[[Media:2025 P4 solutions.pdf| Sol Probs. 4 ]]&nbsp;--> [[Media:2025_Parisi_scheme.pdf| Notes: Probing states with replicas]]
* [[T-4| Spin glasses, equilibrium: replicas, the interpretation (Valentina)]] &nbsp;  [[Media:2025 P4 solutions.pdf| Sol Probs. 4 ]]&nbsp;  
[[Media:2025_Parisi_scheme.pdf| Notes: Probing states with replicas]]
|-valign=“top"
|-valign=“top"
| Week 5 (17/02)
| Week 5 (16/02)
|
|
* [[L-5| Depinning and avalanches (Alberto)]]
* [[T-5| Rugged landscapes: counting metastable states (Valentina)]] &nbsp;<!--[[Media:2025 P5 solutions.pdf| Sol Prob.5 ]]-->
|   
|   
* [[L-6| Bienaymé-Galton-Watson processes (Alberto)]]
* [[T-6| Rugged landscapes: stability of metastable states (Valentina)]] <!--[[Media:2025 P666 solutions .pdf| Sol Prob.6 ]]-->
|-valign=“top"
|-valign=“top"
| Week 6 (03/03)
 
| Week 6 (02/03)
|
|
* [[T-5| Rugged landscapes 1/2: counting local minima (Valentina)]] &nbsp;<!--[[Media:2025 P5 solutions.pdf| Sol Prob.5 ]]-->
* [[LBan-IV| Driven Disordered Materials (Alberto)]]
|   
|   
* [[T-6| Rugged landscapes 2/2: random matrices (Valentina)]] <!--[[Media:2025 P666 solutions .pdf| Sol Prob.6 ]]-->
* [[LBan-V| Avalanches in Disordered Materials (Alberto)]]
|-valign=“top"
|-valign=“top"
| Week 7 (10/03)
 
| 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=“top"
|-valign=“t0p"
| Week 8 (17/03)
 
| 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]]
* [[T-8| Localization on Bethe lattice: 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 ]]-->
* [[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]]-->
|-valign=“top"
|-valign=“top"
| Week 9 (24/03)
| Week 9 (23/03)
|
|
* [[T-9| Localization on Bethe lattice (2/2): 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]]
* [[L-8| Localization in 1D, transfer matrix and Lyapunov exponent (Alberto)]] [[https://colab.research.google.com/drive/1ZJ0yvMrtflWNNmPfaRQ8KTteoWfm0bqk?usp=sharing| notebook]]
|   
|   
* [[L-9|Multifractality, tails (Alberto)]]
* [[L-9|Multifractality, tails (Alberto)]]
Line 121: Line 134:
[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]-->


= Exercises, evaluation and exam =


The exam will be written. A part of it will be based on the exercises below.


= Evaluation and exam =
<li> Week 1: [[Media:Exercises_1-3.pdf| Exercises 1-3 on extreme value statistics]]
</li>


The students have two possibilities:
<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:
[[XX| Exercises 13-15 on dynamics and localization]]
</li>
 
<li> Week 8:
[[XX| Exercises 16-17 on localization]]
</li>
 
<!--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 the Jussieu campus, Room 101, Tours 14 - 24, from 2pm to 5pm.'''-->

Latest revision as of 17:33, 26 February 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)

Notes: Probing states with replicas

Week 5 (16/02)
Week 6 (02/03)
Week 7 (9/03)
Week 8 (16/03)
Week 9 (23/03)


Exercises, evaluation and exam

The exam will be written. A part of it will be based on the exercises below.

  • 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 dynamics and localization
  • Week 8: Exercises 16-17 on localization
    • Retrieved from "http://www.lptms.universite-paris-saclay.fr//wikids/index.php?title=Main_Page&oldid=4150"