Arbeitsgruppe Geometrie

Mathematical Physics II: Mathematical Statistical Mechanics   (SS 2013)

Schedule

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

Office hours

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.

News

• Last Tutorial on 03.07.
• No lecture in the week 8-12.07.
• Here are two examples of partition functions: Example 1 and Example 2.
• Here is an interesting reading: the Kac ring.
• Here is another (very) interesting reading: first chapter of the book ''Short treatise of Statistical Mechanics" by G. Gallavotti (see here for the whole book).
• Here is something about the thermodynamic limit and Van Hove interactions.

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 sheets

• Worksheet 1 (Due: 30.04.13)
• Worksheet 2 (Due: 15.05.13)
• Worksheet 3 (Due: 22.05.13)
• Worksheet 4 (Due: 29.05.13)
• Worksheet 5 (Due: 05.06.13)
• Worksheet 6 (Due: 12.06.13)
• Worksheet 7 (Due: 19.06.13)
• Worksheet 8 (Due: 26.06.13)
• Worksheet 9 (Due: 03.07.13). This is the last homework!

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.