Critical Phenomena
Tuesday & Friday, 11:15-13:00, kHS Pw 12 [LSF]
Prerequisites: quantum mechanics, classical field theory, statistics, basic knowledge of QFT useful
Content of lecture series
In the lecture course an introduction to the theory of critical
phenomena is given. Critical phenomena are relevant for
physics at all scales, and have been studied within a variety of
approaches.
The lecture course aims at giving both, an overview of the methods
applied to the physics of critical phenomena, as well as a survey of
interesting applications.
- Outline in key words
-
Introduction:
Phase transitions, correlation functions, critical exponents, universality
- Landau
theory:
Gaussian model, Ginzburg-Landau hamiltonian, Ginzburg criterion
- Renormalisation group:
block spins, fixed points, critical surface, beta-functions, non-universal aspects
- Methods:
Transfer matrix, epsilon-expansion, 1/N expansion, integrability, functional RG equations, simulations, ...
- Applications:
Ising model, Heisenberg model, O(N)-models, non-linear sigma models, phase structure of selected physics phenomena; e.g. Polymer chains, magnetism, superconductivity, early universe, ...
Literature
| Amit, Martin-Mayor | Field Theory, the Renormalization Group, and Critical Phenomena | World Scientific | |
| Binney, Dowrick, Fisher, Newman | The Theory of Critical Phenomena, an Introduction to the Renormalization Group | Clarendon Press, Oxford | |
| Cardy | Scaling and Renormalization in Statistical Physics | Cambridge UP | |
| Le Bellac | Quantum and Statistical Field Theory | Cambridge UP | |
| Mussardo | Statistical Field Theory | Oxford UP | |
| Parisi | Statistical Field Theory | Addison-Wesley | |
| Yeomans | Statistical Mechanics of Phase Transitions | Oxford UP | |
| Zinn-Justin | Quantum Field Theory and Critical Phenomena | Oxford UP | |
| Zinn-Justin | Phase transitions and Renormalisation Group | Oxford UP |