Topics in Mathematical Statistical Mechanics

What it is about

You will learn the mathematical foundations of statistical mechanics and acquire tools to treat thermodynamic limits, Gibbs states and large deviations. You will also examine phase transitions and symmetry breaking using concrete model examples such as the Ising and O(N) models.

What you will be able to do

• Understanding of Gibbs ensembles and thermodynamic potentials
• Application of convexity and Legendre transform principles
• Knowledge of the existence of the thermodynamic limit and the large deviation principle
• Familiarity with Gibbs equilibrium states
• Explanation of phase transitions and symmetry breaking in examples
• Fundamental properties of the Ising model and O(N) models

What the module consists of

• VorlesungConveying theoretical concepts and motivating example analyses
• ÜbungDeepening the content through exercises, worksheets and solutions for self-check

Teaching method

• Vortrag mit Beispielenfor presenting the content and stimulating autonomous analysis
• Diskussionfor clarifying open questions and deepening understanding
• Übungsaufgaben mit Lösungenfor independent deepening and checking learning success