LFU:online

Absolvents should acquire the abilities to understand and express the contents of the course.

Statistical mechanics is a branch of physics that study systems with large number of elements. Classical examples, among others, are a glass of water (more than 10^23 molecules),  pice of iron (more than 10^23 atoms), population dynamics (around 10^9 people), cars on highway or  a porous stone. Giving an exact description of such systems is a very hard (e.g.  for water one needs to understand, at least 10^23 equations). Instead, one can provide a probabilistic description. Each elements has a random behaviour and the system is describe by very few parameters. We are interested in a large-scale behaviour of such systems (e.g. for water we are interested whether it is solid, liquid or gas). Often, for such systems we observe a phase transition, where a small change of a parameter leads to completely different macroscopic behaviour (e.g. think of a water around 0°C)

During this course, we will present and study some basic mathematical models from the statistical mechanics. One of the most important such model is an Ising model. Initially, introduce as a model for ferromagnetism, it has become one of the most important model in statistical physics with many applications (e.g. thermodynamics, neuroscience, study melt ponds on Artic sea ice, etc.). We will also describe the relation of the Ising model with other models (e.g. FK-percolation, etc.)

The aim of this course is to provide a mathematical background and then a rigours study of the models mentioned above. In particular, we will show the existence of the phase transition in the 2D Ising model.

Hausaufgaben, Vortrag, Beurteilung aufgrund eines einzigen Prüfungsaktes am Ende der Lehrveranstaltung. 

Statistical Mechanics of Lattice Systems: a Concrete Mathematical Introduction  Sacha Friedli and Yvan Velenik

Lectures on the Ising and Potts models on the hypercubic lattice  Hugo Duminil-Copin

Stochastics 1, Stochastics 2, Complex Analysis

No prior knowledge in physics is required