A Criterion for Ferromagnetism in the Isotropic Quantum Heisenberg Model

TL;DR

This paper proposes a new criterion for establishing ferromagnetism in the isotropic quantum Heisenberg model, aiming to rigorously prove the phase transition through spectral analysis of the Hamiltonian.

Contribution

It introduces a novel criterion for ferromagnetism and outlines a proof strategy involving spectral information in invariant subspaces.

Findings

Spectral analysis is key to understanding ferromagnetic phase transitions.

A new criterion for ferromagnetism is proposed.

The approach may simplify rigorous proofs of phase transitions.

Abstract

A criterion for ferromagnetism is presented suggesting a line of proof to rigorously establish the phase transition. Spectral information will be required in certain invariant subspaces of the Hamiltonian, hopefully the relatively crude estimates needed will be not too difficult to establish.