Model of antiferromagnetic superconductivity

We present a simple model that supports coexistent superconductive and antiferromagnetic ordering. The model consists of a system of electrons on a simple cubic lattice that move by tunnel effect and interact via antiferromagnetic Ising spin couplings and short-range repulsions: these include infinitely strong Hubbard forces that prevent double occupancy of any lattice site. Hence, under the filling condition of one electron per site and at sufficiently low temperature, the system is an antiferromagnetic Mott insulator. However, when holes are created by suitable doping, they are mobile charge carriers. We show that, at low concentration, their interactions induced by the above interelectronic ones lead to Schafroth pairing. Hence, under certain plausible but unproven assumptions, the model exhibits the off-diagonal long-range order that characterises superconductivity, while retaining the antiferromagnetic ordering.