RMK Darmstadt
Rhein-Main-Kolloquium
Datum: 24.01.2025
Zeit: 15:00–18:00 Uhr
Alexander Glatzman: Title: Phase diagram of the loop O(n) model Phase transitions are natural phenomena in which a small change in an external parameter, like temperature or pressure, causes a dramatic change in the qualitative structure of the object. To study this, many scientists (such as Nobel laureates Pauling and Flory) proposed the abstract framework of lattice models. One of the most famous lattice models is Bermoulli percolation: given an infinite planar graph, each vertex is open with some probability p independently of the others. We show that, for a general class of graphs, the percolation process at p=1/2 exhibits no (unique) infinite connected component. We use this, together with a novel graphical representation, to show that, in a large two-dimensional region of parameters when n is between 1 and 2, the loop O(n) model exhibits macroscopic loops. This behaviour is reminiscent of scale invariance and, thus, is in agreement with a conformal invariance conjecture. Previously, existence of macroscopic loops was known in several sparse regions of parameters, and these are recent works. The difficulty comes from the lack of monotonicity with respect to parameters: each point of the phase diagram should be treated separately. This is joint work with Matan Harel and Nathan Zelesko (Northeastern).
Yvan Velenik: Title: Interfacial phenomena in the planar Ising model: an overview of nonperturbative results Abstract: I'll review a selection of results about the behavior of interfaces in the planar Ising model obtained during the last three decades. These will include scaling limits of the interface, the phenomena of wetting and critical prewetting, equilibrium crystal shapes and the effect of a gravitational field. The focus will be on nonperturbative results valid in the whole phase coexistence regime.
ReferentInnen
- Yvan Velenik, Universität Genf
- Alexander Glazman, Universität Innsbruck
Ort
- TU Darmstadt S1|05 Raum 24 (Maschinenhaus)
- Magdalenenstraße 12, 64289 Darmstadt
Veranstalter
- Technische Universität Darmstadt
Fachbereich Mathematik - Stochastik
Schlossgartenstraße 7
64289 Darmstadt
Telefon: +49 6151 16-23380
Telefax: +49 6151 16-23381
info(at)stochastik-rhein-mainde
Kooperationspartner
Goethe-Universität Frankfurt am Main, Johannes Gutenberg-Universität Mainz