Ferromagnetism in the Hubbard Model { Examples from Models with Degenerate Single-electron Ground States

Whether spin-independent Coulomb interaction can be the origin of a realistic ferromag-netism in an itinerant electron system has been an open problem for a long time. Here we study a class of Hubbard models on decorated lattices, which have a special property that the corresponding single-electron Schrr odinger equation has N d-fold degenerate ground states. The degeneracy N d is proportional to the total number of sites jj. We prove that the ground states of the models exhibit ferromagnetism when the electron ll-ing factor is not more than and suuciently close to 0 = N d =(2 jj), and paramagnetism when the lling factor is suuciently small. An important feature of the present work is that it provides examples of three dimensional itinerant electron systems which are proved to exhibit ferromagnetism in a nite range of the electron lling factor.