2003/01/31 by Hal Tasaki · 2 citations
Materials Science · Mathematics · Physics and Astronomy · #Magnetic and transport properties of perovskites and related materials #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #cond-mat.str-el #math-ph #math.MP
paper · pdf · doi:10.1007/s00220-003-0952-z
34 pages (References have been added in v2. Many small changes have been made in v3. Minor typos fixed in v4.)
arxiv created 2003/06/27 · openalex publication_date 2003/10/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
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 introduce a class of Hubbard models in any dimensions which are nonsingular in the sense that both the Coulomb interaction and the density of states (at the Fermi level) are finite. We then prove that the ground states of the models exhibit saturated ferromagnetism, i.e., have maximum total spins. Combined with our earlier results, the present work provides nonsingular models of itinerant electrons with only spin-independent interactions where low energy behaviors are proved to be that of a ``healthy'' ferromagnetic insulator.