Ferromagnetism in the Hubbard models with degenerate single-electron ground states

We study a class of Hubbard models in which the corresponding single-electron ground states have bulk degeneracy. We prove that the ground states of the models exhibit ferromagnetism when the electron filling factor is not more than and sufficiently close to ${\mathrm{\rho }}_0$=‖V‖/2‖Λ‖ (where ‖V‖ is the dimension of degeneracy and ‖Λ‖ is the number of sites), and exhibit paramagnetism when the filling factor is sufficiently small. This is the first time that a three-dimensional itinerant-electron system is proved to exhibit ferromagnetism in a finite range of the electron filling factor.