## 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 modeling 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

If you are interested in statistical modelling and biophysics, the

in condensed matter physics, but also far beyond the traditional realm of physics, for instance in the modeling 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

If you are interested in statistical modelling and biophysics, the

*Seminar on Statistical Biology: Epidemiological and evolutionary modeling of an infectious disease - The case of Covid-19*may also be of interest to you. See here for details.### Schedule

The course will start on 2.11. For the time being, the entire course will take place online.
Lectures will be pre-recorded. We will do tutorials and question-and-answer sessions via Zoom.
On specific weeks to be announced we will have question-and-answer sessions, and inverted-classroom sessions.
These will take place on Thursdays at 10am via Zoom. The first dates are 12.11,19.11,26.11, for
further dates check the calendar on Ilias and announcements on the Slack channel.

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. Initially, all tutorial classes will take place online. We will switch some of them to a "face-to-face" format as soon as conditions allow. You can already choose between the two types of classes now. Details are available on this ILIAS page.

Exam: 19.02.2021, 13:00 - 16:00

Retake: 31.03.2021, 12:30 -15:30

The exam will take place online. Details are posted on the Slack channel.

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. Initially, all tutorial classes will take place online. We will switch some of them to a "face-to-face" format as soon as conditions allow. You can already choose between the two types of classes now. Details are available on this ILIAS page.

Exam: 19.02.2021, 13:00 - 16:00

Retake: 31.03.2021, 12:30 -15:30

The exam will take place online. Details are posted on the Slack channel.

### Resources and teaching materials

The central resource for lectures, lecture notes, and problem sets is the ILIAS page
here.

For an informal exchange of information, we have also opened a slack channel for this lecture course. See this ILIAS page for an invitation link.

Below, you find 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

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.

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

For an informal exchange of information, we have also opened a slack channel for this lecture course. See this ILIAS page for an invitation link.

Below, you find 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

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.

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

### 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.

The picture above shows a uniform lattice of several types of polygons by Rziff, see here for details and licensing.