The course will focus on a general development of the renormalization group (RG) as a systematic way to explore the large scale ``emergent'' behaviour of different types of systems. Technical aspects of RG will be discussed by considering specific cases, like, polymers, quantum systems, and critical phenomena. The approach taken will help us to see how RG can lead to a proper description of a system, avoiding any prior knowledge of its phenomenology. We shall start with the real space RG, and then go over to various avatars of the field theoretic RG.
If time permits, special topics to be discussed include,
the Kosterlitz--Thouless transition (xy model), critical dynamics, nonequilibrium systems.
Basic statistical mechanics (at the level of Reif or Pathria).
Elementary notions of diffusion, random walks (though not essential)
No prior knowledge of phase transitions or critical phenomena needed.
RG results will be used to explore the nature of the critical point.
1. Chaikin-Lubensky covers most of the topics,
2. D. Amit's book is complementary to Ref. 1.
3. McComb: Renormalization Methods
4. Cardy: Scaling and Renormalization in Statistical Physics
5. Kardar: Statistical mechanics of fields
6. relevant reviews and papers.