Course Unit Page

Academic Year 2020/2021

Learning outcomes

At the end of the course the student will learn the foundations of the physics of phase transitions and critical phenomena, within a framework common to Statistical Mechanics and Quantum Field Theory. He/she will be able to understand the physics of systems with an infinite number of degrees of freedom non-perturbatively through the methods of the renormalization group. The student will also be able to discuss and solve related physical problems.

Course contents

Review of Statistical Mechanics and Phase transitions

  • general concepts and partition function
  • First and second order phase transitions
  • order parameter, correlation length
  • correlation functions, scaling behaviour
  • critical exponents and universality classes
  • Landau Ginzburg theory
  • the Ising model

Field Theory and Statistical Mechanics

  • link between Quantum Field Theory and Statistical Mechanics
  • renormalization group
  • spontaneous symmetry breaking

Conformal Field Theory

  • Conformal Group in D dimensions. The D=2 case. Example of the free massless boson.
  • Classical conformal algebra in D=2. Quantum Ward Identities and Virasoro Algebra.
  • Operator product expansions. Classification of states and fields. Conformal bootstrap.
  • Verma moduli, null vectors and degenerate representations. Minimal models.
  • Examples of universality classes in D=2 for minimal models.


  1. G. Mussardo, Statistical Field Theory, Oxford Univ. Press
  2. P. Di Francesco, P. Mathieu, D. Sénéchal, Conformal Field Theory, Springer, Berlin
  3. K. Huang, Statistical Mechanics, John Wiley & Sons, New York
  4. R. Baxter, Exactly solved models in Statistical Mechanics, Academic Press, London
  5. P. Ginsparg, Applied Conformal Field Theory, Les Houches lectures 1988 - arXiv:hep-th/9108028 [http://arxiv.org/abs/hep-th/9108028]
  6. L.H. Ryder, Quantum Field Theory, Cambridge Univ. Press
  7. C. Itzykson and J.-M. Drouffe, Statistical Field Theory, Cambridge Univ. Press

Teaching methods

Theoretical topics are fully explained in class by the teacher.
Some classes will be devoted to exercises that students will solve under the teacher's supervision.

Further exercises will be proposed on the IOL site as personal training.

Assessment methods

Oral exam.
Questions will cover both the theoretical part and the exercises treated in class.

Teaching tools

Text and solution of applications and exercises studied in class.

Office hours

See the website of Francesco Ravanini

See the website of Davide Fioravanti