Advanced Statistical Mechanics and Disordered Systems
A.Y. 2023/2024
Learning objectives
Undefined
Expected learning outcomes
Undefined
Lesson period: Open sessions
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Course syllabus
- Probability and Statistical Physics. Universality theorems for independent random variables, Large Deviations, Maximum Entropy and ensemble theories.
- "50 Shades of Mean-Field". Different mean-field approaches, as approxi- mations, algorithms, theories, and models (focused on spin systems).
- Disordered systems, spin glasses and optimization problems.
- Density expansions and equation of state. Mayer function. Diagrammatic method. Second virial coefficient.
- Radial distribution function. Approximate integral equations. The Percus- Yevick equation.
- Exact solution of the Percus-Yevick equation. Beyond the Percus-Yevick approximation.
- "50 Shades of Mean-Field". Different mean-field approaches, as approxi- mations, algorithms, theories, and models (focused on spin systems).
- Disordered systems, spin glasses and optimization problems.
- Density expansions and equation of state. Mayer function. Diagrammatic method. Second virial coefficient.
- Radial distribution function. Approximate integral equations. The Percus- Yevick equation.
- Exact solution of the Percus-Yevick equation. Beyond the Percus-Yevick approximation.
Prerequisites for admission
Knowledge of elementary statistical mechanics would be required to attend seamlessly this class, although the course will strive to be self-contained.
Teaching methods
A number of diverse teaching strategies will be put at work, including traditional lectures, active study and reading group material, and exercises.
Teaching Resources
1. Luca Peliti, Statistical Mechanics in a Nutshell (Princeton University Press 2009)
2. James Sethna, Statistical Mechanics: Entropy, Order Parameters, and Complexity (Oxford, 1st ed. 2006, 2nd ed. 2021)
3. Hidetoshi Nishimori, Statistical Physics of Spin Glasses and Information Processing: An Introduction (Clarendon Press 2001)
4. Andrés Santos, A Concise Course on the Theory of Classical Liquids: Basics and Selected Topics (Springer 2016)
5. Jean-Pierre Hansen and Ian R. McDonald, Theory of Simple Fluids with Applications to Soft Matter (London Academic Press 4th ed. 2013)
2. James Sethna, Statistical Mechanics: Entropy, Order Parameters, and Complexity (Oxford, 1st ed. 2006, 2nd ed. 2021)
3. Hidetoshi Nishimori, Statistical Physics of Spin Glasses and Information Processing: An Introduction (Clarendon Press 2001)
4. Andrés Santos, A Concise Course on the Theory of Classical Liquids: Basics and Selected Topics (Springer 2016)
5. Jean-Pierre Hansen and Ian R. McDonald, Theory of Simple Fluids with Applications to Soft Matter (London Academic Press 4th ed. 2013)
Assessment methods and Criteria
The final exam is an oral test, based on an individual project, which consists in reproducing theoretically and computationally a preassigned topic. The oral examination is divided into two parts
1. Formal presentation (using blackboard and/or slides) of the project, clearly explaining the question and its motivations, the methods employed, and the results achieved.
2. Questions, free discussion and deepening of the points that emerged during the presentation.
1. Formal presentation (using blackboard and/or slides) of the project, clearly explaining the question and its motivations, the methods employed, and the results achieved.
2. Questions, free discussion and deepening of the points that emerged during the presentation.
FIS/02 - THEORETICAL PHYSICS, MATHEMATICAL MODELS AND METHODS - University credits: 6
Lessons: 48 hours
Professor:
Cosentino Lagomarsino Marco
Professor(s)
Reception:
By appointment, in-person and via Teams or other platforms.