Random loop approaches to quantum spin systems

Daniel Ueltschi (University of Warwick)

Tuesday 29th October 16:00-17:00 Maths 311B

Abstract

Quantum spin systems are used to describe the magnetic properties in condensed matter physics. I will introduce a family of models that include the ferromagnetic and antiferromagnetic Heisenberg models, and derive their random loop representations. I will review some rigorous results (mainly for three-dimensional lattices), conjectures, and open questions.

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