Ferrimagnetic long-range order of the Hubbard model

In this paper, we show rigorously that there exists the ferrimagnetic long-range order in the ground state of the positive-U Hubbard model at half filling on some bipartite lattices. When ${\mathit{N}}_{\mathit{A}}$>${\mathit{N}}_{\mathit{B}}$(${\mathit{N}}_{\mathit{A}}$ and ${\mathit{N}}_{\mathit{B}}$ are the total site numbers of two sublattices A and B), except for the ferromagnetism which was found by Lieb [Phys. Rev. Lett. 62, 1201 (1989)], there also exists the antiferromagnetic long-range order in the ground state. This result only requires U>0 and is independent of the dimension of the lattices.