Random loops and quantum spin systems
by Prof. Jakob Björnberg (University of Gothenburg)
at IHES ( Salle du Conseil )
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.
|Organisé par||Hugo Duminil-Copin|