Reflection positivity and infrared bounds for quantum spin systems
arXiv:2204.12896
Abstract
The method of reflection positivity and infrared bounds allows to prove the occurrence of phase transitions in systems with continuous symmetries. We review the method in the context of quantum spin systems.
28 pages, 2 figures. This article is dedicated to Elliott Lieb on the occasion of his 90th birthday. In the revised version the case of long-range interactions is simplified (the method of Frohlich, Israel, Lieb, Simon applies). We also added a reference to Koma and Tasaki, who proved that long-range order implies non-differentiability of the free energy