Course Identification

The course will deal with the following topics:

Equilibrium statistical physics: Phase transitions and critical phenomena; mean-field theories;

Ising type models; renormalization group approach; Kosterlitz-Thouless type transitions; correlation functions.

Dynamics and nonequilibrium statistical physics: linear response; Langevin approach; fluctuation-dissipation relation; Fokker-Planck equation; models of driven systems.

Upon successful completion of this course students should be able to:

1. Recall the basic notions of thermodynamics and statistical physics from a new deductive perspective.
2. Describe the basics of statistical physics from the viewpoint of information theory so that the students will be able to see unity of different disciplines in science and engineering (statistical physics, information theory, coding theory) as all dealing with decision-making under an incomplete information.
3. Discuss interacting systems and phase transitions.
4. Appreciate how competition of order and disorder determines the properties of systems at different space dimensionalities, how the renormalization group framework explains universality of critical phenomena and why the random walk is central to our understanding of fluctuating fields.
5. Understand the topological phase transitions.

Lecture notes part 1

Basic books:

1. L. D. Landau and E. M. Lifshitz, Statistical Physics Part 1.
2. R. K. Pathria, Statistical Mechanics.
3. R. Kubo, Statistical Mechanics.
4. K. Huang, Statistical Mechanics.
5. H. Callen  Thermodynamics

Course reading:

1. S K Ma Modern Theory of Critical Phenomena  The Bejamin Cummings Publishing Co
2. D J Amit Field Theory Renormalization Group and Critical Phenomena  World Scientific
3. L. Peliti  Statistical Physics in a Nutshell
4. M. Kardar Statistical Physics of Fields
5. M. Kardar Statistical Physics of Particles