![Logo M2 avec PSL](/sites/default/files/styles/partenaire/public/2023-11/Logo%20M2%20avec%20PSL_0.png?itok=DOOgpM1L)
Statistical Field Theory and applications
This course is about how to describe complex systems using ideas of the renormalization group (‘coarse-graining’) and statistical field theory.
![](/sites/default/files/inline-images/output_1.png)
This course is about how to describe complex systems using ideas of the renormalization group (‘coarse-graining’) and statistical field theory. Taking lattice models of magnetism as a starting point, we will explore a few milestones of 20th century many-body physics, such as Wilson-Fisher fixed point and Kosterlitz-Thouless transition.
We will explore
— Examples of scale invariance
— Real space renormalization group
— Renormalization group formalism
— Applications of Landau Ginsburg theory and mean field
— Free field theory (as a conformally invariant fixed point)
— The large n limit in the O(n) model
— Wilson-Fisher 4-epsilon expansion
— Nonlinear sigma model and 2+epsilon expansion
— Field theory duality (XY model and Sine-Gordon)
— Kosterlitz Thouless RG flows
— The ‘landscape’ of the O(n) model in various dimensions
— Mapping between quantum and classical statistical mechanics
We will touch on further topics such as gauge theory and topological order if time allows.
![](/sites/default/files/inline-images/image_5.png)
Basic concepts from statistical mechanics such as partition function, phase transition, symmetry breaking. Familiarity with the idea of a functional (field) integral. Gaussian integration.
Written final exam and homework problem sets (3-4 submissions throughout the semester).
- John Cardy, Scaling and Renormalization in Statistical Physics, Cambridge University Press
- Denis Bernard, Statistical Field Theory and Applications, An Introduction for (and by) Amateurs https://www.phys.ens.fr/~dbernard/Documents/Teaching/Lectures_Stat_Field_Theory_vnew.pdf
- Mehran Kardar, Statistical Physics of Fields, Cambridge University Press