87962 - Statistical Field Theory

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

Part 1 (module 2, Prof. L. Piroli)

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

Part 2 (module 1, Prof. F. Ravanini)

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.

Readings/Bibliography

The material corresponding to the lectures, in the form of notes or slides used by the teachers, is available on the course's "Virtuale" page.

In addition to this, it is recommended to read about the topics covered in the following texts:

1. G. Mussardo, Statistical Field Theory, Oxford Univ. Press
2. J. Cardy, Scaling and renormalization in statistical physics, Cambridge university press, 1996.
3. P. Di Francesco, P. Mathieu, D. Sénéchal, Conformal Field Theory, Springer, Berlin
4. M. Kardar, Statistical physics of fields. Cambridge University Press, 2007.
5. K. Huang, Statistical Mechanics, John Wiley & Sons, New York
6. R. Baxter, Exactly solved models in Statistical Mechanics, Academic Press, London
7. P. Ginsparg, Applied Conformal Field Theory, Les Houches lectures 1988 - arXiv:hep-th/9108028 [http://arxiv.org/abs/hep-th/9108028]
8. L.H. Ryder, Quantum Field Theory, Cambridge Univ. Press
9. 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

Traditional oral exam at the blackboard: 2 or 3 questions chosen by the teacher on topics covered in class. The evaluation will take into account the clarity of presentation and the student's mastery of the subject.

Teaching tools

The lectures are presented mainly with slides, complemented by explanations at the blackboard.

A few exercises will be proposed in some of the subjects treated, by using the tools present on the Virtuale web page.

Office hours

See the website of Francesco Ravanini

See the website of Lorenzo Piroli