Antiferromagnetic correlation in the half-filled strongly correlated electron models at nonzero temperature: A rigorous result

As an extension of our previous rigorous investigation on the spin correlations in the ground states of the half-filled Hubbard model and the periodic Anderson model [G. S. Tian, Phys. Rev. B >50, 6246 (1994)], in the present paper we study the behavior of these correlation functions at finite temperature. We show rigorously that, at any T≠0, the predominant spin correlations in these systems are antiferromagnetic. Furthermore, based on this result, we also show that a quasi-one (or two)-dimensional itinerant electron ferrimagnet must have a gapless branch of ferromagnetic excitations. This conclusion is consistent with the previous results derived by the spin-wave theory