Random loops and quantum spin systems

par Prof. Jakob Björnberg (University of Gothenburg)

mercredi 6 déc. 2017, 16:30 → 17:30 Europe/Paris

Salle du Conseil (IHES)

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 Z^d 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.