Correlation inequalities for classical and quantum XY models

TL;DR

This paper reviews correlation inequalities in classical and quantum XY models, establishing bounds on their critical temperatures and comparing them to Ising models, with implications for understanding phase transitions.

Contribution

It provides a comprehensive review of correlation inequalities for XY models and introduces an explicit lower bound on the quantum XY model's critical temperature.

Findings

Critical temperature of XY models is lower than that of Ising models.

Established an explicit lower bound for the quantum XY model's critical temperature.

Confirmed the inequalities hold in both classical and quantum cases.

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.