## Scaling, Criticality and the Renormalization Group in Statistical Physics (PH2292)

Winter 2022/23

Lecturer: Johannes Knolle

Teaching Assistants: TBA

**Lectures:**

Monday 12:00–14:00, PH 3344

Wednesday, 08:00–10:00, PH 1121

**Tutorials:**

TBD

**Outline:**

Statistical mechanics is the branch of physics in which statistical methods are employed to understand how a large number of simple microscopic constituents of a system give rise to macroscopic properties. In this course we will study the universal features of phase transitions.

The course focuses on the the renormalization group (RG) framework to describe a whole range of different paradigmatic systems. For example, we will learn how to apply the RG scheme to understand criticality and universal scaling in Percolation, the Ising model, the Phi-4 theory, the Kosterlitz-Thouless transition and in disordered systems.

The following topics are covered in this module:

- The general theory of the renormalization group
- Percolation theory as an introduction to the scaling hypothesis and RG
- Block spin RG and Widom scaling in the Ising model
- Effective field theory and perturbative RG (Wilson-Fisher fixed point)
- Non-linear sigma models
- XY model and the Kosterlitz-Thouless transition (Coulomb liquid RG)
- Disorder effects on phase transitions

**Literature:**

- K. Christensen and N.R. Moloney, Complexity and Criticality. Imperial College Press, 2005.
- J.M. Yeomans, Statistical Mechanics of Phase Transition, OUP 1992.
- J. Cardy, Scaling and Renormalization in Statistical Physics, CUP 1996.
- M. Kardar, Statistical Physics of Particles, CUP 2007.
- P.M. Chaikin and T.C. Lubensky, Principles of Condensed Matter Physics, CUP 1995.