On the alloy analogy approximation of the hubbard Hamiltonian

It is not well established that the ground state of the Hubbard Hamiltonian is not always paramagnetic. It is also well established that the ground state of the alloy analogy approximation of the non-degenerate Hubbard Hamiltonian is always paramagnetic. It has been claimed on the other hand that the ground state of the alloy analogy approximation of the doubly degenerate Hubbard Hamiltonian is not always paramagnetic. We show in this article that this last statement is not fully proved. Contradictory results are in fact obtained, depending upon the physical quantity one computes: total energy calculations have indeed been reported showing a magnetic instability while we prove here that magnetic susceptibility calculations do not. We conclude therefore that the ground state of the alloy analogy approximation of the doubly degenerate Hubbard Hamiltonian is not known at the present time.