# Tilman Enss | Teaching — Statistical Physics

as of 16 July 2017

## Statistical Physics (MVSeminar)

#### Summer term 2017

**This theory seminar introduces advanced topics in classical and quantum statistical physics, such as phase transitions, critical phenomena, and renormalization.
It builds on the Theoretical Statistical Physics (MKTP1) lecture in the previous semester.**

Supervisor: Priv.-Doz. Dr. Tilman Enss and Dr. Naoto Tanji

general objectives of advanced mandatory seminars (page 18)

Fri 11.15-13.00h, Philosophenweg 19, SR
[LSF]

#### Seminar Topics

**2017-04-21: Random Walks**[M. Haas]

A particle hopping at random on a lattice exhibits diffusive motion. The seminar explains that this motion is governed by a conservation law and can be described by a hydrodynamic equation.

*Kadanoff, ch. 5*

seminar notes (for participants only)**2017-04-28: Superfluids**[S. Zundl]

A superfluid can flow without dissipation: a famous example is^{4}He at low temperature. The seminar introduces this quantum liquid and its excitations to explain the phenomenon of superfluidity.

*Huang, ch. 13.1-7*

seminar notes (for participants only)

**2017-05-05: Dilute Bose Gas**[C. Wahl]

Many bosons can condense into a single quantum state to form a Bose-Einstein Condensate; excitations in the BEC can be described by Bogoliubov theory.

*Huang, ch. 13.8; Pitaevskii, ch. 4*

seminar notes (for participants only)

**2017-05-12: Ising Model**[L. Spieß]

The Ising model is one of the paradigms of statistical physics and describes phase transitions in magnetic systems. In one dimension it can be solved exactly with the transfer matrix technique.

*Huang, ch. 14*

seminar notes (for participants only)

**2017-05-19: Phase transitions**[C. Alexa]

This seminar gives an overview over phase transitions of first and second order, using magnets as an example.

*Kadanoff, ch. 10-11.2 and parts of ch. 4*

seminar notes (for participants only)

**2017-06-02: Critical Phenomena**[D. Michels]

Near the critical point of a phase transition, many different physical systems exhibit universal behavior. The approach to the critical point is governed by scaling relations.

*Huang, ch. 16; Kadanoff, ch. 11.3-6*

seminar notes (for participants only)

**2017-06-09: Landau-Ginzburg Theory**[R. Carlucci]

The Landau-Ginzburg theory is a very successful description how the (coarse-grained) order parameter behaves near a phase transition.

*Huang, ch. 17; Cardy, ch. 3*

seminar notes (for participants only)

**2017-06-16: Real-Space Renormalization**[V. Dinh]

The real-space decimation provides a particularly simple example of a renormalization procedure, which corresponds to zooming successively out; one can then identify fixed points which do not change under this transformation.

*Cardy, ch. 2; Kadanoff, ch. 13, parts of ch. 4; Huang, ch. 18.1—18.4*

seminar notes (for participants only)

**2017-06-23: Wilson Renormalization**[J. Urban]

In the Wilsonian renormalization group, instead, one works in momentum space and includes fluctuations in successively smaller momentum shells.

*Huang, ch. 18.5+*

seminar notes (for participants only)

**2017-06-30: XY Model and Spin Waves**[D. Lafferty]

The planar XY model has continuous "magnetic compasses" at each lattice site, instead of the discrete Ising spins. Its excitations are spin waves, and in low dimensions they can fluctuate so strongly that they destroy long-range order.

*Kadanoff, ch. 16*

seminar notes (for participants only)

**2017-07-07: Kosterlitz-Thouless Transition**[H. Böhringer]

In addition to spin-wave excitations, the rotors can align to form vortices, or topological excitations. One can also think of these vortices as charges in a Coulomb gas. When vortices unbind at higher temperature, they drive the Kosterlitz-Thouless phase transition.

*Kadanoff, ch. 17*

seminar notes (for participants only)

**2017-07-14: Transverse Ising Model**[J. Fronk]

When one puts an Ising ferromagnet in a transverse magnetic field, there are quantum tunneling processes which may destroy the ferromagnetic order. When this happens, there is a quantum phase transition in the ground state, which affects the physical properties in an extended region of the phase diagram.

*Sachdev, ch. 4; Enss, ch. 8.1*

#### Literature

- Cardy, Scaling and Renormalization in Statistical Physics, Cambridge Univ. Press 1996
- Enss, Condensed Matter Theory lecture notes 2016 (download for participants)
- Huang, Statistical Mechanics, Wiley 1963
- Kadanoff, Statistical Physics: Statics, Dynamics and Renormalization, World Scientific 2000
- Pitaevskii and Stringari, Bose-Einstein Condensation, Clarendon Press 2003
- Sachdev, Quantum Phase Transitions, Cambridge Univ. Press 1999

#### Prerequisites

- Quantum Mechanics
- Statistical Physics (MKTP1)

#### Formalities

- Oral presentation (blackboard or slides) max. 60 minutes, followed by discussion.
- Hand in writeup until three weeks after your seminar: an essay of 12 pages on your seminar topic, with short abstract, introduction, exposition of your topic, conclusion, careful citations and bibliography. (Don't just paste your slides but write full sentences and use sketches/figures as appropriate.)
- You can earn 6 credit points. The grade is composed of the oral presentation, the writeup, and your participation in the discussions.
- Attendance is mandatory; please send me an email if you are ill.
- It is recommended that we go over your talk together before your presentation; please make an appointment for, say, the Monday before your talk.