**Advanced Statistical Physics**

**Lecturer: **Prof. dr. M. I. Katsnelson

Room HG03.062, phone 52995

**♦
**30 hours lecture, 30 hours tutorial

**♦
Required knowledge**: Bachelor Course “Statistical
Physics”

**♦ Goals: **The course
is focused on the concepts of order parameter, broken symmetry and scaling,
with applications to solid state and soft condensed matter physics. General
methods of theoretical physics such as path integrals and renormalization group
are considered in a context of statistical physics.

**♦
Subjects**

**• **Landau theory of phase transitions and the concept of order
parameter. Examples: structural phase transitions, magnetism, liquid crystals,
superconductivity, superfluidity.

**• **Ginzburg-Landau theory; the role of fluctuations. Correlation length.

**• **Concepts of scaling for the second-order phase transitions and its
qualitative justification

(“Kadanoff decimation”).

**• **

**• **Order parameter, broken symmetry and topological defects.

**• **Fluctuations in low-dimensional systems and Mermin-Wagner theorem.
Berezinski-Kosterlitz-Thouless transition.

**• **Scaling concepts in polymer physics. Scaling properties of a single
polymer chain.

**• **Introduction to the statistical physics of membranes.

**♦
Literature**

**• **S.-K. Ma. Modern
theory of critical phenomena.

**• **J. J. Binney, N.
J. Dowrick, A. J. Fisher, and M. E. J. Newman. The theory of critical
phenomena. An introduction to the renormalization group.

**• ** P.-G. de Gennes. Scaling
concepts in polymer physics.