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Phase transitions and critical phenomena

Informations pratiques


Discipline :

Physique

Niveau :

Master 2

Semestre :

S3b

Crédits ECTS :

6

Volume Horaire :

24h Cours
10h TD

Responsable :

Jean-Louis Barrat

Université Joseph Fourier, Laboratoire Interdisciplinaire de Physique (Grenoble)

Intervenants :

Jean-Louis Barrat
Thierry Biben

This course is also part of the Erasmus Mundus ATOSIM curriculum, and may therefore be given in English

Objectives

The successful theoretical explanation of experiments on phase transitions was one of the major achievements of Statistical Mechanics in the second half of the 20th century. Experiments show remarkable features, such as irrational critical exponents and universality among groups of apparently radically different systems. The understanding of these features required the introduction of concepts that go beyond the classical mean field picture, and highlighted the importance of fluctuations, scaling and correlation lengths, which are now part of the common language in many problems in statistical physics and beyond. Calculation of critical exponents was made possible by the development of the elegant renormalization group approach. In this procedure, behaviour on microscopic length scales is shown to be irrelevant and can be "integrated out", leaving effective interactions that are independent of scale and are functions of only a few "universal" parameters.

Course outline

1. Brief review of thermodynamics and models

2. The mean field approach
Mean-field spirit: Curie-Weiss, Variational, Bethe lattice (percolation), Maier Saupe, classical density functional theory.

3. Landau theory

4. The Landau-Ginzburg free energy and some applications
Interfaces, Topological defects, Ornstein-Zernike

5. Beyond mean field, correlations and fluctuations

6. Scaling approaches

7. Renormalisation: principle and some examples

8. Dynamics of phase transitions
Nucleation, spinodal decomposition, critical slowing down, mode-coupling

Bibliographie

- P. Chaikin, T.Lubensky, "Principles of Condensed Matter Physics"
- Cours de M. Héritier au DEA de physique des solides (Paris 1997-1998) : http://cel.archives-ouvertes.fr/cel-00092939
- Julia M. Yeomans, "Statistical Mechanics of Phase Transitions"
- Nigel Goldenfeld, "Lectures On Phase Transitions And The Renormalization Group"

Pré-requis

interactions et transitions de phase M1

Modalité de l'examen

Écrit (in English ou en français)