Scaling, Criticality and the Renormalization Group in Statistical Physics (PH2292)
Winter 2022/23

Lecturer: Johannes Knolle
Teaching Assistants: TBA

Monday 12:00–14:00, PH 3344
Wednesday, 08:00–10:00, PH 1121



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


  • 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.

TUM course website PH2292