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.
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.
- H. Duminil-Copin and V. Tassion: A new proof of the sharpness of the phase transition for Bernoulli percolation on $\mathbb Z^d$, Ens. Math. (2016).
- H. Duminil-Copin and V. Tassion: A new proof of the sharpness of the phase transition for Bernoulli percolation and the Ising model, Commun. Math. Phys. (2016).
- H. Duminil-Copin, A. Raoufi and V. Tassion: Sharp phase transition for the random-cluster and Potts models via decision trees, Ann. Math. (2019).
- H. Duminil-Copin, A. Raoufi and V. Tassion, Subcritical phase of d-dimensional Poisson-Boolean percolation and its vacant set. Ann. H. Lebesgue (2020).
- H. Duminil-Copin, S. Goswami, P.F. Rodriguez and F. Severo: Equality of critical parameters for percolation of Gaussian free field level-sets. Preprint.
- M. Aizenman and H. Duminil-Copin: Marginal triviality of the scaling limits of critical 4D Ising and $\varphi^4$ models. Ann. Math. (2021).
- Beekenkamp, Thomas: Sharp phase transitions in percolation models. Dissertation, LMU München: Faculty of Mathematics, Computer Science and Statistics, 2021.
||Workshop in Garching
||Sharp phase transition for percolation
||Sharp phase transition for the Ising model
||Percolation, Ising, Potts, and the random cluster model
||Sharp phase transition via OSSS - I
||Sharp phase transition via OSSS - II
||4D Ising model - 1
||4D Ising model - 2
||4D Ising model - 3