(52469) Advanced Statistical Mechanics: Critical and Non-Equilibrium Phenomena


Winter term 2017-2018

Prof. Dr. F. Evers, Dr. Daniel Hernangómez Pérez


  • First lecture starts on October, 16
  • Graded exercise sessions start the following week (from October, 23)
  • Lecture on October, 20 has been cancelled. You are encouraged to attend the Hofstadter Butterfly Symposium!
  • Lecture on November, 3 is cancelled and will be recovered on October, 26 in extraordinary location PHY 5.1.03 and time 8:30 – 10:00
  • Lectures on November, 27; December, 1; December, 4 have been cancelled and will be recovered on November, 24; December, 8; December, 15 in extraordinary location PHY 5.1.03 and time 8:30 – 10:00
  • Course is dismissed. Thank you for your participation!

Lectures (4 SWS)

Monday, 10:00 – 12:00, Room: PHY 5.0.20
Friday, 10:00 – 12:00, Room: PHY 5.0.20

Exercises (2 SWS)

Thursday, 17:00 – 19:00, Room:  PHY 5.1.03




A very important goal of theoretical physics is a to provide a general framework for cathegorizing physical phenomena. To this end, the most powerful instruments that have been developed over the last decades are classical and quantum field theories. They provide transparent concepts for a classification of the different phases of matter in terms of symmetries (“actions”) with the associated phase diagrams and fixed point structures.

The lecture offers a pedestrian way into the field. It will be highlighted, in particular, how field theories can help to understand the universal connections between seemingly so different phenomena as magnetism, superconductivity and the liquid-water transition. None but least, they also provide key insights answering the most fundamental question of why it is that we can describe the macroscopic world with only very few parameters and observables despite of so many degrees of freedom entering the Schroedinger equation.


This course presumes the following background: equilibrium statistical mechanics and elementary condensed matter physics. Notions of classical field theory can be helpful although they are not required.


1. Construction of a field theory in condensed matter systems: Ising model

1.1 Mean-field theory and self-consistent field (SCF) theory
1.2 Fluctuation contributions to physical observables
1.3 Breakdown of mean-field theory

2. Critical phenomena: universality and scaling

2.1 Momentum shell renormalization group
2.2 Epsilon-expansion
2.3 Applications

3. Topological Defects

3.1 Kosterlitz-Thouless transition

4. Quantum phase transitions at zero temperature

4.1 Wilson-scheme for itinerant electrons
4.2 The non-linear sigma model

5. Hydrodynamics

5.1 Dynamical correlations and response functions
5.2 Diffusion
5.3 Langevin theory
5.4 Hydrodynamics of simple fluids


Recommended texts

  1. Principles of Condensed Matter,
    P. M. Chaikin and T. Lubensky, Cambridge University Press (2000). 
  2. Quantum Many-Particle Systems,
    J. W. Negele and H. Orland, Advanced Books Classics (1998). 
  3. A Modern Approach to Phase Transitions,
    I. Herbut, Cambridge University Press (2007) 

Further reading

  1. Statistical Theory of Heat - Nonequilibrium Phenomena,
    W. Brenig, Springer (1989). 
  2. Quantum Phase Transitions,
    S. Sachdev, Cambridge University Press (2011). 
  3. Scaling and Renormalization in Statistical Physics,
    J. Cardy, Cambridge University Press (1996). 

Exercise Sessions

General Rules

Problem solving is crucial to really understand the material taught in the lectures. Therefore, you should try to work out the exercises by yourselves. In order to motivate you to do so, the following rules apply:

  • Each week there will be an exercise sheet.
  • At the beginning of each exercise session, you check in the list which problems are you prepared to present on the blackboard.
    Based on that list, one student will be randomly selected (uniform probability distribution) to present her/his solution.
  • In order to participate in the final exam, you have to check at least 50% of the total points over the course of the semester.
  • Academic integrity: Cheating will not be tolerated!

Exercise Sheets

  • Sheet 1 - Discussion: October, 26.
  • Sheet 2 - Discussion: November, 2.
  • Sheet 3 - Discussion: November, 9.
  • Sheet 4 - Discussion: November, 16.
  • Sheet 5 - Discussion: November, 23.
  • Sheet 6 - Discussion: November, 30.
  • Sheet 7 - Discussion: December, 14.
  • Sheet 8 - Discussion: January 11 (Christmas Sheet).
  • Sheet 9 - Discussion: January, 18.


Last modified: 27th Jul, 2018 by Daniel Hernangomez