A note on ferromagnetism in the Hubbard model on the complete graph

TL;DR

This paper clarifies the conditions under which ferromagnetism occurs in the Hubbard model on the complete graph, emphasizing known rigorous results for specific electron numbers and discussing their implications.

Contribution

It explains existing rigorous results on ferromagnetism in the Hubbard model on the complete graph for certain electron counts, clarifying the current understanding.

Findings

Ferromagnetism is rigorously established for N_e=N-1 in the Hubbard model on the complete graph.

The paper clarifies the implications of these results for the broader understanding of the model.

It emphasizes that the problem does not require further publication beyond this explanatory note.

Abstract

Recently there have appeared some papers which discuss the existence of ferromagnetism in the Hubbard model defined on the complete graph. At least for the special electron number N_e=N-1, where N denotes the number of sites in the lattice, the existence of ferromagnetism in this model was established rigorously some time ago, as special (and indeed the simplest) cases of more general classes of models. Here we explain these implications to clarify the situation, although we believe the implications are straightforward. We are posting this note to the preprint archive to make it public, but we are not planning to publish it in other forms. This is because we do not think the problem warrants any extra publications, and we believe that the validity of our explanation is evident to the readers.