Hauptseminar Symplektische Geometrie

Johanna Bimmermann, Universität Heidelberg

We will give a discussion on the two dimensional Ising model and present a solution using a Grassmann integral. The Grassmann integral can be interpreted as a discrete path integral. This way spin correlation functions of the Ising model can be cal- culated. In the second part we will look at dimer models on planar graphs and introduce the FKT algorithm to represent their partition functions as pfaffians. It will be shown that the Ising model can be mapped on a dimer model. The last part will investigate phase transitions of dimer models on bipartite periodic graphs in a constant external field. As an outlook we will present a theorem of Richard Kenyon, Andrei Okounkov and Scott Sheffield that identifies phase diagrams with amoebas.

Montag, den 30. Juli 2018 um 15:00 Uhr, in Mathematikon, INF 205, SR 4 Montag, den 30. Juli 2018 at 15:00, in Mathematikon, INF 205, SR 4

Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Benedetti