Possible coexistence of antiferromagnetism and superconductivity in the Hubbard model

The Hubbard model in the nearly half-filled case was studied in the mean field approximation using the effective Hamiltonian approach. Both antiferromagnetic order parameter and condensation of singlet pairs were considered. In certain parameter range the coexistence of antiferromagnetism and superconductivity is energetically favorable. In this paper relations to the high temperature superconductivity and other theoretical approaches are discussed