Content: Contrary to its name, the seminar addresses both Bachelor and Master students and the subjects of most talks can serve as starting points for Bachelor theses. There will also be talks on more advanced subjects that can lead to Master theses.

We will study lattice models from statistical mechanics, with a particular emphasis on phase transitions. The basic question in statistical mechanics is "How can we explain physics on the observable, macroscopic scale from the processes occurring on the molecular, microscopic scale?", and we will get a small glimpse into this field.

After discussing basic concepts of thermodynamics, we will focus mostly on simple microscopic stochastic lattice systems that serve as toy models for physical processes. By "zooming out" from the atomistic to the observable scale we can derive laws of thermodynamics as mathematical theorems, rather than postulating them.

Our guiding example will be the Ising model, a toy model for a magnet, and we will study its phase transition at the critical temperature: If a ferromagnet is heated above a critical temperature, it loses its magnetic properties. But we will also discuss a simpler mean field approximation (Curie-Weiss model). Further subjects could be lattice gases (a toy models for ideal gases), percolation (a toy models for a porous medium), or, more advanced, interacting particle systems.

You can find more information on the seminar website.

Literature

Our main reference is the book

Friedli, Velenik - Statistical Mechanics of Lattice Systems (Cambridge University Press, 2017).

https://www.unige.ch/math/folks/velenik/smbook/

Additional information

Prerequisites: Stochastics I and II. No knowledge from physics or more advanced probability is needed!
Target audience: Advanced Bachelor students, BMS students, Master students.