Outline of part A

TD2: Nematic liquid crystals
TD3: Renormalization group: uses and applications
     A family of energetically equivalent + 1 topological defects;      same with -1 topological defects;      same with a +1/-1 pair of defects

(exam 2016-2017) Statistical mechanics at the edge : Lee and Yang zeros     solution    
(exam 2017-2018) Circling again with Lee and Yang     solution    
(exam 2018-2019) A moving scheme : renormalization à la Migdal-Kadanoff     solution    
(exam 2019-2020) The Potts model         solution    
(exam 2020-2021) Finite-size scaling     solution

Part B, M2 condensed matter + quantum physics: Frédéric van Wijland
Part B, M2 soft matter: Martin Lenz

Bibliography

Introduction to Modern Statistical Mechanics, D. Chandler, Oxford University Press
Statistical Mechanics of Phase Transitions, J. Yeomans, Oxford Science Publications
Principles of Condensed Matter Physics, P. Chaikin and T. Lubensky, Cambridge
Introduction to Statistical Field Theory, E. Brézin, Cambridge
Scaling and Renormalization in Statistical Physics, J. Cardy, Cambridge
Des phénomènes critiques aux champs de jauge, M. Le Bellac, EDP Sciences

In case some gaps need to be filled in complex analysis, linear algebra, probability theory...
Mathematics for Physics and Physicists, W. Appel, Princeton University Press
and for the gaps in basic stat mech / thermodynamics
Thermodynamics and an Introduction to Thermostatistics, H. Callen, John Wiley and Sons, or see Chandler's and Yeomans' books above

Some useful document / answser to questions raised during class

A simple proof of Perron-Frobenius theorem for symmetric matrices
    There is a flaw in the argument... where?
van der Waals equation: critical exponents
Direct relevance of Ising model: from magnetic systems to real neurons paper 1   paper 2   paper 3   paper 4   paper 5   paper 6
Ising 1D : transfer matrix with a magnetic field
Lecture 2, the challenge (Mermin Wagner)
Correlation function (and length) of Ising 1D ; solution
Landau m²/m⁴/m⁶, temperatures T^* and T^**
Why naive mean-field can fail
Scattering measure of local order in a fluid (from Chandler)
Requires the notion of pair correlation function, g(r)
Scaling hypothesis and scaling relations
Scaling relations from RG treatment