Topics in Modern Statistical Physics

This course provides an introduction to selected topics of statistical physics. The focus wil be on the theory of phase transitions in condensed matter systems, both quantum and classical. The students entering the course are expected to have completed an introductory lecture of statistical physics and thermodynamics as well as the standard undergraduate level courses (classical and quantum mechanics, electrodynamics). Some familiarity with the formalism of second quantization will be useful, but is not required.

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The course comprises two parts. The first part focuses on the theory of classical systems undergoing phase transitions. The second part is devoted to the equilibrium quantum many-body problem.

1) Basic notions: universality, scaling, critical indices, symmetry-breaking, classifications of phase transitions.

2) Classical model systems: the Ising, XY and Heisenberg models; van der Waals fluids.

3)Landau theory.

4) Widom scaling hypothesis.

5) Renormalization theory in real space.

6) Momentum-shell renormalization.

7) Path-integral formulation of the quantum many-body problem.

8) Perturbation theory in the quantum many-body problem

9) Broken symmetry and collective phenomena

- interacting electron gas,

- Bose-Einstein condensation and superfluidity,

- Superconductivity.

1. M. Kardar "Statistical Physics of Fields",

2. N. Goldenfeld "Lectures on Phase Transitions and the Renormalization Group",

3. J. Cardy, "Scaling and Renormalization in Statistical Physics",

4. J. W. Negele, H. Orland, "Quantum Many-Particle Systems",

5. A. Altland, B. Simons " Condensed Matter Field Theory",

6. D. Amit, "Field Theory, the Renormalization Group, and Critical Phenomena".

This course provides both the overview of selected problems of modern statistical physics (both quantum and classical) and a variety of methods to solve such problems.

Written and oral exam.