Béatrice De Tilière (IUF, University Paris Dauphine CEREMADE)
Wednesday, April 21, 2021 - 14:00
Online Kolloquium
Karl-Liebknecht-Str. 24/25, 14469 Potsdam
The Ising model belongs to the field of statistical mechanics and models ferromagnetism. Its Z-invariant version is defined on a planar, embedded graph satisfying a geometric constraint known as isoradiality, imposing that all faces can be inscribed in a circle of radius 1. Z-invariance imposes that the coupling constants satisfy the Ising model Yang-Baxter equations. The "classical" Ising models on the square, triangular or honeycomb lattice are specific examples of the above. The coupling constants are explicit, and depend on an elliptic parameter k playing the role of the temperature; in the specific case where k=0, the Ising model is critical. In this talk we will define the model, and explain how it can be studied using dimers, also known as perfect matchings, of a related graph. We will then report on results obtained in collaboration with Cédric Boutillier (Sorbonne University) and Kilian Raschel (University of Tours). We will discuss the locality property of the Gibbs measure and of the free energy and establish that the model undergoes an order two phase transition at k=0, showing that this phase transition is the same as that of the rooted spanning forests model. This talk is aimed at a general audience; the models as well as the statistical mechanics terminology will be defined.
submitted by Sylke Pfeiffer (sypfeiffer@math.uni-potsdam.de)