## Advanced Statistical Physics

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

find application in condensed matter physics, but also far beyond the traditional realm of physics, 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.

find application in condensed matter physics, but also far beyond the traditional realm of physics, 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.

- 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: Tuesday 14:00-15:30 in lecture
theater III and Thursday 10:00-11:30 in the seminar Room of
Physics Institute I

First lecture 15.10 14:00 in lecture theater III

Exercises: Monday, 12:00-13:30 seminar room of Physics Institute II

Exam: Lecture theatre I, 11.02.2014 at 13:00.

Retake: Lecture theatre III, 05.04.2014 at 9:00

The exam results are available here, the results of the retake are here. Email jb for further information.

First lecture 15.10 14:00 in lecture theater III

Exercises: Monday, 12:00-13:30 seminar room of Physics Institute II

Exam: Lecture theatre I, 11.02.2014 at 13:00.

Retake: Lecture theatre III, 05.04.2014 at 9:00

The exam results are available here, the results of the retake are here. Email jb for further information.

### Teaching material

Here you find Mathematica notebooks showing the behaviour of
analytical solutions of systems covered in this course.

To view the results you can use the free Wolfram CDF Player (500Mb, sorry!). To explore the solution further on your own, use the computers in the CIP-lab, which run Mathematica.

Ising model in 1D

Ising model in 2D

Weiss' model of the ferromagnet

Dominik Derigs has produced an animation of the free energy function of the 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, which we used in class, lets you explore different boundary conditions. This one here lets you change both the temperature and the magnetic field (try it!).

To view the results you can use the free Wolfram CDF Player (500Mb, sorry!). To explore the solution further on your own, use the computers in the CIP-lab, which run Mathematica.

Ising model in 1D

Ising model in 2D

Weiss' model of the ferromagnet

Dominik Derigs has produced an animation of the free energy function of the 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, which we used in class, lets you explore different boundary conditions. This one here lets you change both the temperature and the magnetic field (try it!).

### Literature

J. Cardy, Scaling and Renormalization in Statistical Physics,
Cambridge University Press

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. Kardar, Statistical Physics of Fields, Cambridge University Press

G. Mussardo, Statistical Field Theory, Oxford University Press

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

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

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. Kardar, Statistical Physics of Fields, Cambridge University Press

G. Mussardo, Statistical Field Theory, Oxford University Press

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

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

The picture above was created by Lauro Chieza de Carvalho, see here for details and licensing. The picture is not actually meant to show a lattice of spins (but a lattice of clocks).