Metallic ferromagnetism: Progress in our understanding of an old strong-coupling problem

TL;DR

This paper reviews recent progress in understanding metallic ferromagnetism, highlighting its stability in the Hubbard model across various dimensions and the conditions that favor its emergence.

Contribution

It provides a comprehensive review of recent theoretical advances in the microscopic understanding of metallic ferromagnetism, especially in the Hubbard model.

Findings

Ferromagnetism is stable in the Hubbard model for dimensions 1, 2, and infinity.

Progress has been made in understanding the microscopic conditions for ferromagnetism.

Differences between single-band and orbitally degenerate cases are discussed.

Abstract

Metallic ferromagnetism is in general an intermediate to strong coupling phenomenon. Since there do not exist systematic analytic methods to investigate such types of problems, the microscopic origin of metallic ferromagnetism is still not sufficiently understood. However, during the last two or three years remarkable progress was made in this field: It is now certain that even in the one-band Hubbard model metallic ferromagnetism is stable in dimensions $d=1,$ 2, and $\infty$ on regular lattices and at intermediate values of the interaction $U$ and density $n$. In this paper the basic questions and recent insights regarding the microscopic conditions favoring metallic ferromagnetism in this model are reviewed. These findings are contrasted with the results for the orbitally degenerate case.