Correlation inequalities for classical and quantum XY models

Abstract

We review correlation inequalities of truncated functions for the classical and quantum XY models. A consequence is that the critical temperature of the XY model is necessarily smaller than that of the Ising model, in both the classical and quantum cases. We also discuss an explicit lower bound on the critical temperature of the quantum XY model.

13 pages. Submitted to the volume "Advances in Quantum Mechanics: contemporary trends and open problems" of the INdAM-Springer series, proceedings of the INdAM meeting "Contemporary Trends in the Mathematics of Quantum Mechanics" (4-8 July 2016) organised by G. Dell'Antonio and A. Michelangeli

References in corpus (3)

• Finite-Temperature Néel Ordering of Fluctuations in a Plaquette Orbital Model
• Local disorder, topological ground state degeneracy and entanglement entropy, and discrete anyons
• Correlation inequalities for the quantum XY model

Cited by in corpus (2)

• An elementary proof of phase transition in the planar XY model
• On the duality between height functions and continuous spin models