Introduction to Statistical Field Theory

Course description

In many areas of physics, such as high energy physics, gravitation, and in statistical and condensed matter physics, it is necessary to understand the collective effects of a large number of degrees of freedom. Quantum field theory is the language that has been developed to describe the physics in such apparently different fields. In this course we will stress the applications to statistical physics and discuss:

  • Critical phenomena, Landau theory, fluctuations and Ginzburg criterion.
  • Scaling behavior, introduction to Wilson renormalization group.
  • Relation with renormalization theory in perturbative quantum field theory
  • Some applications in statistical physics, condensed matter and soft matter.

Learning outcome

The student should be able to understand and explain the use of advanced techniques in statistical physics. This includes:

  • The concept of phase transitions in simple models as well as the physics at or near critical points.
  • The renormalization group and the flow to infrared fixed points.
  • Landau’s Fermi-liquid theory.
  • BCS superconductivity


  • Quantum and Statistical Field Theory
    Michel Le Bellac, Oxford Science Publications, Clarendon Press; 1 edition (May 21, 1992)
  • Lectures On Phase Transitions And The Renormalization Group
    Nigel Goldenfeld, Frontiers in Physics, Addison-Wesley (July 21, 1992)
  • Statistical Field Theory
    Claude Itzykson, Jean-Michel Drouff, Cambridge Monographs on Mathematical Physics, Cambridge University Press (March 29, 1991)