31921 - Statistical Mechanics 2

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

PART 1 (Prof.ssa Ercolessi)

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

- Theory of phase transitions, critical exponents and universality classes, spontaneous symmetry breaking, the Ising model.

- Hartree-Fock approximation: variational technique and applications to particle gases.

- Superconductivity: phenomenology, BCS microscopic theory,  Ginzburg-Landau approach.

- Ginzburg Landau Theory for the O(N) model: order parameter, correlations and critical exponents.

 

PART 2 (Prof. 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

[1] G. Morandi, F. Napoli, E. Ercolessi, Statistical Mechanics, World Scientific. 

[2] R.K. Pathria, P.D. Beale, Statistical Mechanics, Elsevier.

[3] J. F. Annett, Superconductivity, Superfluids and Condensates, Oxford.

[4] L.H. Ryder, QuantumField Theory, Cambridge 

[5] P. Di Francesco, P. Mathieu, D. Sénéchal - Conformal Field Theory - Springer

[6] P. Ginsparg - Applied Conformal Field Theory - Les Houches lectures 1988 - arXiv:hep-th/9108028

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 Elisa Ercolessi

See the website of Francesco Ravanini