University of Heidelberg

Tilman Enss | Teaching — Advanced Statistical Physics

as of 30 September 2021

Advanced Statistical Physics (MVSpec)

Winter term 2021/22

This advanced theory course introduces paradigmatic models of statistical physics and their critical properties near phase transitions. In particular, we shall discuss the Heisenberg and O(N) vector models, the nonlinear sigma model, the XY model, the Sine-Gordon model, and the spherical model. By computing their critical behavior, one can understand the phase transitions in many different systems in statistical physics, condensed matter physics and beyond, which belong to the same universality classes. We will use field theoretic methods and introduce renormalization, epsilon and 1/N expansions, and duality transformation.


  1. Landau theory and O(N) vector model
  2. Renormalization group and universality
  3. Nonlinear sigma model and epsilon expansion
  4. Topological excitations in the XY and Sine-Gordon models and the Kosterlitz-Thouless transition
  5. Spherical model and quantum phase transitions
Lecture materials (for participants)

Dates and Location

Lecture Tuesday and Thursday 09.15-11.00h, Philosophenweg 12, kHS starting Oct 19 [LSF]
Exercise Monday 14.15-16.00h, Philosophenweg 12, R 105 starting Oct 25
Please register for access to lecture materials and to take the exam.


  • Theoretical Statistical Physics (MKTP1)
  • working knowlegde of phase transitions and field theoretical language


As an introduction, the lecture notes by Mudry are recommended; Mudry chapter 1 introduces the field theoretical language.
For starters:

  • Cardy, Scaling and Renormalization in Statistical Physics, Cambridge University Press (1996)
  • Mudry, Lecture Notes on Field Theory in Condensed Matter Physics, World Scientific (2014)
Further reading:
  • Altland and Simons, Condensed Matter Field Theory, Cambridge University Press (2010)
  • Negele and Orland, Quantum Many-Particle Systems, Addison-Wesley (1988)
  • Zinn-Justin, Phase Transitions and Renormalization Group, Oxford University Press (2007)


The written exam will be held in the week of February 14-18, 2022. Those who pass will obtain 8 credit points. In order to participate in the exam you need to be registered for the course; you may unregister yourself before February 4.