 Fakultät II
Institut für Mathematik

# Arbeitsgruppe Geometrie Geometry Group

Members

Projects

Lehre
Verlaufspläne:
Bachelor
Diplom
Vergangene Semester

Seminare

Images, Videos, and Games

Virtual Math Labs

Software

## Mathematical Physics II: Mathematical Statistical Mechanics   (SS 2013)

### Schedule

 Lectures Tutorial Prof. Yu.B. Suris Mon 12:15 - 13:45 MA 645 Prof. Yu.B. Suris Wed 12:15 - 13:45 MA 744 Dr. M. Petrera Wed 10:15 - 11:45 MA 651

This is a course of the Berlin Mathematical School held in English.

### Office hours

 Name Office hours Room Prof. Yu.B. Suris -------------------------------- MA 827 Dr. M. Petrera Monday 12:00 - 14:00 MA 819

### Contents

• Principles of statistical mechanics, Elements of probability theory.

• Gibbs measure, Partition function, Thermodynamic limit, Phase transitions, Asymptotic Gibbs measure.

• Classical spin models, Curie-Weiss model, Ising model, Transfer matrix method, Star-triangle relation.

### Tutorial

• Tutorial 1 (24.04.13): Sigma algebras, probability spaces, entropy, exercises on probability.
• Tutorial 2 (08.05.13): Boltzmann transport equation, Maxwell distribution, gas law, continuous and discrete systems.
• Tutorial 3 (15.05.13): Gibbs ensembles, canonical ensemble, partition function, ideal gas.
• Tutorial 4 (22.05.13): Thermodynamic limit, Van Hove interactions, stability of thermodynamics, correction of Ex. 3 WS2.
• Tutorial 5 (29.05.13): One-dimensional Ising model (partition function, free energy), exercise on an arbitrary spin, correction of WS3.
• Tutorial 6 (05.06.13): Gibbs ensembles for two-dimensional Ising-type models.
• Tutorial 7 (12.06.13): Gibbs ensembles for two-dimensional Ising-type models, correction of Ex. 3 WS5.
• Tutorial 8 (19.06.13): Exercises, correction of WS 6.
• Tutorial 9 (26.06.13): Partition function of the two-dimensional Ising-Onsager model, exercises.
• Tutorial 10 (03.07.13): Correction of WS 9.

### Homework policy

• Homework assignments are due weekly at the beginning of the Wed. lecture (10:15). They have to be turned in directly to the lecturer. No homework will be accepted after the deadline has passed.

• Homework assignments can be solved in groups of three people.

• To get the Übungsschein, you need to satisfactorily complete 60% of the homework assignments.

 Matteo Petrera . 29.06.2013