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.




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”).


Wilson theory of the phase transitions: renormalization group and ε-expansion.


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.