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Phase diagram of quantum spin systems with S=1 and SU(2)-invariant interactions
Probability| Speaker: | Daniel Ueltschi, University of Warwick |
| Location: | 2112 MSB |
| Start time: | Wed, Feb 17 2016, 4:10PM |
Description
Systems of spin 1 have a rich phase diagram that includes
ferromagnetic, antiferromagnetic, and spin nematic phases (in
dimensions three and higher). They can be studied with the help of
graphical (random loop) representations, introduced by Tóth and
Aizenman, Nachtergaele. The existence of phase transitions can be
proved using the method of reflection positivity and infrared bounds
of Fröhlich, Simon, Spencer. I will explain a recent conjecture about
the joint distribution of the lengths of long loops
("Poisson-Dirichlet") and how this conjecture helps to identify the
extremal Gibbs states.