Rigorous aspects of equilibrium statistical mechanics - Département de Physique de l'Ecole Normale supérieure

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Rigorous aspects of equilibrium statistical mechanics

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Faculties: Jérémie BOUTIER and Guilhem SEMERJIAN
Chargé de TD :
ECTS credits: 12

Description

Statistical mechanics study systems made of a large number of interacting elementary degrees of freedom. Its most salient predictions concern the existence of phase transitions, i.e. of singularities of the macroscopic properties of such systems when an external parameter (the temperature in particular) is tuned across a threshold value.

This discipline has obviously its roots in physics. However its models are also studied in mathematics, mainly in probability and combinatorics. The goal of this course will be to give an introduction to some rigorous results in mathematical statistical mechanics. One part of it will be devoted to the general properties of finite dimensional models (existence of the thermodynamic limit for the free-energy, stability conditions, Gibbs measures) and their relationship, in an appropriate limit, with the mean-field approximations. A particular emphasis will be given to bidimensional models (percolation, Ising, Potts, dimers, self-avoiding walks) for which several exact results can be obtained via combinatorical methods. Several tools of enumerative and analytic combinatorics, which have a wider range of application, will be introduced along the way.

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Next student seminar :
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Here you can find information about your internships:
Experimental Internship - Undergraduate program
Master ICFP first year Internship

News : ICFP Research seminars
November 14 - 18, 2022 :
All information about the program

Contact us - Student support and Graduate School office :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr