7 J an 2 00 3 Ferromagnetism in the Hubbard model — A constructive approach —

It is believed that strong ferromagnetic orders in some solids are generated by subtle interplay between quantum many-body effects and spin-independent Coulomb interactions between electrons. Here we describe our rigorous and constructive approach to ferromagnetism in the Hubbard model, which is a standard idealized model for strongly interacting electrons in a solid. We present, for the first time, a class of nonsingular Hubbard models in any dimensions which are proved to exhibit saturated ferromagnetism. (Here a nonsingular model means a many electron system in which neither Coulomb interaction nor the density of states at the Fermi level is infinite.) Combined with our earlier results, the present work provides nonsingular models of itinerant electrons where low energy behaviors are proved to be that of a healthy ferromagnetic insulator. [email protected], http://www.gakushuin.ac.jp/̃ 881791/ 1