University of Heidelberg

Tilman Enss | Teaching — Advanced Statistical Physics

as of 5 November 2020

Advanced Statistical Physics (MVSpec)

Winter term 2020/21

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, as time permits. 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 Thursday 11.15-13.00h, Philosophenweg 12, gHS starting Nov 5 online-only for the month of November [LSF]
Please register for access to lecture materials and to take the exam.

This two-hour lecture-only course is planned to take place on campus and lecture materials will be made available online for registered participants who cannot attend in person.


  • 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 on Thursday, 25 February 2021, from 11:15-12:00h. Those who pass will get 4 credit points. In order to participate in the exam you need to be registered for the course; you may unregister yourself before February 18.