by Prof. Jakob Björnberg (University of Gothenburg)

Salle du Conseil (IHES)

Salle du Conseil


Le Bois-Marie 35, route de Chartres 91440 Bures-sur-Yvette

A variety of spin systems, including Heisenberg and XXZ models, can be represented in terms of random loops in d+1 dimensions. The (conjectured) phase transitions are expressed in terms of the occurrence of macroscopic loops. Moreover, the macroscopic loops are expected to obey a Poisson--Dirichlet distribution. For Zd such results are lacking. Here we present progress on mean-field models: on the complete graph and on regular tress. Based on ongoing work with Jürg Fröhlich and Daniel Ueltschi.