31921 - Statistical Mechanics 2

Academic Year 2016/2017

  • Teaching Mode: Traditional lectures
  • Campus: Bologna
  • Corso: Second cycle degree programme (LM) in Physics (cod. 8025)

Learning outcomes

At the end of the course, the student knows the mathematical concepts at the foundation of statistical mechanics and is able to study analytically a large class of interacting models, including their critical phenomena.

Course contents

We will study the theoretical foundations of classical and quantum statistical mechanics also for interacting systems.

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
  • renormalization group
  • the Ising model

Ginzburg Landau Theory

  • link between Quantum Field Theory and Statistical Mechanics
  • Landau Ginzburg theory
  • 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.

Readings/Bibliography

  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
  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.

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