Exact results on ferromagnetism in correlated electron systems

Abstract

Exact results, both old and new, on the stability of saturated ferromagneiism in the Hubbard model and its extensions are discussed. For the Hubbard model with all nearest-neighbor interactions a new set of rigorous criteria, valid at half filling, is derived and a generalization of Nagaoka's theorem to finite interactions is presented. Of all coupling parameters only the on-site and the exchange interaction are found to be essential. At strong coupling comparison with the effective t — J model is made. Further extensions, e.g. to the band-degenerate case, are discussed.