Vanishing critical magnetization in the quantum Ising model

TL;DR

This paper demonstrates that the magnetization in the quantum Ising model disappears at the critical point, extending classical results to quantum systems using graphical methods and infrared bounds.

Contribution

It adapts classical Ising model techniques to prove vanishing magnetization at criticality in the quantum Ising model for specific dimensions.

Findings

Magnetization vanishes at the critical point in the quantum Ising model.

Results apply to ground states in dimensions d≥2.

Results extend to positive-temperature states in dimensions d≥3.

Abstract

Adapting the recent argument of Aizenman, Duminil-Copin and Sidoravicius for the classical Ising model, it is shown here that the magnetization in the transverse-field Ising model vanishes at the critical point. The proof applies to the ground state in dimension $d\geq2$ and to positive-temperature states in dimension $d\geq 3$, and relies on graphical representations as well as an infrared bound.