Department Mathematik



                                      Student Seminar
               Phase transitions in statistical mechanics

                                            Winter semester 2022/23

A fascinating aspect of statistical mechanics is the occurrence of phase transitions: upon continuous variation of a system parameter, the global properties change suddenly and drastically. Despite an enormous body of reserach, the rigorous understanding of phase transitions remains a challenge for mathematicians (and theoretical physicists). In this seminar, we focus on some contributions of Hugo Duminil-Copin and his coauthors, which have shaped the field.

Initially, our attention is on a phenomenon coined as sharp phase transition. We'll discuss two new proof strategies in the context of percolation that were proposed by Duminil-Copin, Raoufi and Tassion, as well as their generalizations to Ising and Potts models. In the later part, and as time permits, we also focus on similar questions on GFF percolation and/or the recently established "Phi-4 triviality" proven by Aizenman and Duminil-Copin.

Target group: Master students in TMP, Mathematics, FIM. Solid background in probability theory and/or stat mech is required.

Lecturers: Sabine Jansen and Markus Heydenreich

Registration: Interested students please (pre-)register by email to Prof. Jansen. Indicate your degree progam, relevant course background, whether you are aiming for 3ECTS or 6ECTS seminar, and paper(s) of interest from the list below.

Time and Format:  weekly meetings on Wednesday, 12-14 in room B040. Schedule below.


An introduction to sharp phase transition for percolation is also given by the following recent thesis:

Planned schedule:

Speaker Topic
10/11 Nov

Workshop in Garching
16 Nov
Sharp phase transition for percolation
23 Nov
Sharp phase transition for the Ising model
30 Nov
Percolation, Ising, Potts, and the random cluster model
07 Dec
Sharp phase transition via OSSS - I
14 Dec 21 Dec
Sharp phase transition via OSSS - II

Christmas break
11 Jan
4D Ising model - 1
18 Jan
4D Ising model - 2
25 Jan

no talk
02 Feb
4D Ising model - 3