Infrared bound and mean-field behaviour in the quantum Ising model

TL;DR

This paper establishes a stronger infrared bound for the quantum Ising model, enabling analysis of mean-field behavior and confirming the critical exponent $$ attains its mean-field value in high dimensions.

Contribution

It introduces a stronger infrared bound for the quantum Ising model, facilitating the study of mean-field critical behavior.

Findings

Critical exponent $=1$ in dimension ≥4 at positive temperature

Critical exponent $=1$ in dimension ≥3 at zero temperature

Logarithmic corrections in boundary cases

Abstract

We prove an infrared bound for the transverse field Ising model. This bound is stronger than the previously known infrared bound for the model, and allows us to investigate mean-field behaviour. As an application we show that the critical exponent $\gamma$ for the susceptibility attains its mean-field value $\gamma=1$ in dimension at least 4 (positive temperature), respectively 3 (ground state), with logarithmic corrections in the boundary cases.