(52469) Advanced Statistical Mechanics: Critical and NonEquilibrium Phenomena
Winter term 20172018
Prof. Dr. F. Evers, Dr. Daniel Hernangómez Pérez
News
 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
Syllabus
Summary
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 liquidwater 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.
Prerequisites
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.
Contents
1. Construction of a field theory in condensed matter systems: Ising model
1.1 Meanfield theory and selfconsistent field (SCF) theory
1.2 Fluctuation contributions to physical observables
1.3 Breakdown of meanfield theory
2. Critical phenomena: universality and scaling
2.1 Momentum shell renormalization group
2.2 Epsilonexpansion
2.3 Applications
3. Topological Defects
3.1 KosterlitzThouless transition
4. Quantum phase transitions at zero temperature
4.1 Wilsonscheme for itinerant electrons
4.2 The nonlinear sigma model
5. Hydrodynamics
5.1 Dynamical correlations and response functions
5.2 Diffusion
5.3 Langevin theory
5.4 Hydrodynamics of simple fluids
Literature
Recommended texts

Principles of Condensed Matter,
P. M. Chaikin and T. Lubensky, Cambridge University Press (2000).
 Quantum ManyParticle Systems,
J. W. Negele and H. Orland, Advanced Books Classics (1998).
 A Modern Approach to Phase Transitions,
I. Herbut, Cambridge University Press (2007)
Further reading
 Statistical Theory of Heat  Nonequilibrium Phenomena,
W. Brenig, Springer (1989).
 Quantum Phase Transitions,
S. Sachdev, Cambridge University Press (2011).
 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.