Thermal stability of the Nagaoka-Thouless theorems

TL;DR

This paper extends the Nagaoka-Thouless theorems to include electron-phonon and electron-photon interactions, demonstrating their robustness in the Hubbard model using path integral methods.

Contribution

It provides a proof that the Aizenman-Lieb theorem on ferromagnetism remains valid with additional electron-phonon and electron-photon interactions.

Findings

The ferromagnetic properties are stable under electron-phonon interactions.

The ferromagnetic properties are stable under electron-photon interactions.

The proof employs path integral representations of partition functions.

Abstract

We prove that the Aizenman-Lieb theorem on ferromagnetism in the Hubbard model holds true even if the electron-phonon interactions and the electron-photon interactions are taken into account. Our proof is based on path integral representations of the partition functions.