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 rho-0 = Absolute value of V /2 Absolute value of LAMBDA (where Absolute value of V is the dimension of degeneracy and Absolute value of LAMBDA 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.