English

Reflection positivity and infrared bounds for quantum spin systems

Mathematical Physics 2022-12-08 v2 math.MP

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.

Keywords

Cite

@article{arxiv.2204.12896,
  title  = {Reflection positivity and infrared bounds for quantum spin systems},
  author = {Jakob E. Björnberg and Daniel Ueltschi},
  journal= {arXiv preprint arXiv:2204.12896},
  year   = {2022}
}

Comments

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

R2 v1 2026-06-24T11:00:13.277Z