Statistical physics

Frédéric van Wijland (MSC, Paris-Diderot), Tobias Kuhn (Physique/Ens), Martin Lenz and Emmanuel Trizac (LPTMS, Paris-Sud/CNRS)

Schedule of the lectures

Mondays, 8.30am - 1pm, Paris-Diderot Campus

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

BibliographyIntroduction 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 classA 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 m^{2}/m^{4}/m^{6}, 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