## Advanced Statistical Physics

Statistical physics describes systems with many interacting degrees of
freedom. Tools and concepts of statistical physics have applications

in condensed matter physics, but also far beyond the traditional realm of physics, for instance in the modelling of biological, economic,

or social systems. This lecture course covers the basic tools of modern statistical physics, as well as the required mathematical apparatus.

A key concept to address fluctuations on different length-scales is the so-called renormalisation group, which emerges as the shared language

between quantum field theory, condensed matter physics, statistical physics, and even cosmology. Particular topics are

in condensed matter physics, but also far beyond the traditional realm of physics, for instance in the modelling of biological, economic,

or social systems. This lecture course covers the basic tools of modern statistical physics, as well as the required mathematical apparatus.

A key concept to address fluctuations on different length-scales is the so-called renormalisation group, which emerges as the shared language

between quantum field theory, condensed matter physics, statistical physics, and even cosmology. Particular topics are

- introduction to stochastic systems
- equilibration and the Boltzmann measure
- lattice models: exactly solvable systems in one and two dimensions; high- and low-temperature expansions; dualities
- the renormalisation group and scaling
- Landau-Ginzburg theory and fluctuations: introduction to the field-theoretic approach
- disordered systems

### Schedule

Lectures take place on Tuesdays 8:00-09:30 and Thursdays 10:00-11:30 in lecture
theater III; the course will start on 11.11. All lectures will also be recorded.

Registration: If you are going to take this class for credit (this is most of you), please sign up on KLIPS2.0. Registering should automatically give you access to the relevant ILIAS page. Otherwise, connect to this ILIAS page and sign up for membership. Use the rider "Sprache" (language) on the top right to set the language to English. Let me know via email if there are technical problems or if you have questions.

There will be weekly tutorial classes, both in person and online. Registration will be via KLIPS.

Exams: 15.2.2024, 13:00 - 16:00

Retake: 20.3.2024, 9:00 -12:00

Both exams will be in Lecture Theatre 1.

Registration: If you are going to take this class for credit (this is most of you), please sign up on KLIPS2.0. Registering should automatically give you access to the relevant ILIAS page. Otherwise, connect to this ILIAS page and sign up for membership. Use the rider "Sprache" (language) on the top right to set the language to English. Let me know via email if there are technical problems or if you have questions.

There will be weekly tutorial classes, both in person and online. Registration will be via KLIPS.

Exams: 15.2.2024, 13:00 - 16:00

Retake: 20.3.2024, 9:00 -12:00

Both exams will be in Lecture Theatre 1.

### Resources and teaching materials

The central resource for lectures and problem sets is the ILIAS page
here. There is also a discussion board where you can ask and answer questions.

Below, I will place Mathematica notebooks on some analytically solvable models addressed in this course, as well as links to applets

and other material of interest. To view the results you can use the free Wolfram CDF Player (500Mb, sorry!). To explore the solutions

further on your own, you can use the Mathematica notebooks (.nb) on the computers in the CIP-lab, which run Mathematica.

Ising model in 1D .cdf .nb .pdf

Ising model in 2D .cdf .nb .pdf

Weiss' model of the ferromagnet .cdf .nb .pdf

There are many applets simulating the 2D-Ising model. This one here lets you change both the temperature and the magnetic field (try it!).

Dominik Derigs (thanks!) has produced an animation of the free energy function of the Curie-Weiss (mean field) ferromagnet, available here.

Watch the parameters beta and h in the bottom right corner.

A handout covering the RG analysis of the Landau-Ginzburg action for the coupling parameter g is available here.

Below, I will place Mathematica notebooks on some analytically solvable models addressed in this course, as well as links to applets

and other material of interest. To view the results you can use the free Wolfram CDF Player (500Mb, sorry!). To explore the solutions

further on your own, you can use the Mathematica notebooks (.nb) on the computers in the CIP-lab, which run Mathematica.

Ising model in 1D .cdf .nb .pdf

Ising model in 2D .cdf .nb .pdf

Weiss' model of the ferromagnet .cdf .nb .pdf

There are many applets simulating the 2D-Ising model. This one here lets you change both the temperature and the magnetic field (try it!).

Dominik Derigs (thanks!) has produced an animation of the free energy function of the Curie-Weiss (mean field) ferromagnet, available here.

Watch the parameters beta and h in the bottom right corner.

A handout covering the RG analysis of the Landau-Ginzburg action for the coupling parameter g is available here.

### Literature

N. Goldenfeld, Lectures on phase transitions and the renormalization
group, Westview Press

N.G. van Kampen, Stochastic Processes in Physics and Chemistry, North Holland

M. Plischke and B. Bergersen, Equilibrium Statistical Physics, World Scientific

(in German) H. Römer and T. Fink, Statistische Mechanik, VCH

The best single book to start with is Kardar. This is the second volume of two. You may also want to look at the first volume

(Statistical Physics of Particles) to refresh your knowledge of elementary statistical physics. The topics of scaling and renormalisation are covered optimally in Goldenfeld.

N.G. van Kampen, Stochastic Processes in Physics and Chemistry, North Holland

**M. Kardar, Statistical Physics of Fields, Cambridge University Press**M. Plischke and B. Bergersen, Equilibrium Statistical Physics, World Scientific

(in German) H. Römer and T. Fink, Statistische Mechanik, VCH

The best single book to start with is Kardar. This is the second volume of two. You may also want to look at the first volume

(Statistical Physics of Particles) to refresh your knowledge of elementary statistical physics. The topics of scaling and renormalisation are covered optimally in Goldenfeld.

Picture credit: A. A. Bjarmason via WikiMedia Commons. The picture shows the formation of ice due to high humidity and low temperatures. Observed February 26, 2005, in Akureyri, Iceland.