Rigorous criteria for ferromagnetism in itinerant electron systems

We derive the first detailed, rigorous criteria for the stability of saturated ferromagnetism in the most general single-band model of itinerant electrons, valid for arbitrary translationally invariant lattices, at half filling. These conditions are given by inequalities for the model parameters. Of all interactions only the on-site and the exchange interactions are found to be essential. By the same approach we also derive rigorous criteria for the stability of saturated ferromagnetism in the Hubbard model with a magnetic field.