Universality of mean-field antiferromagnetic order in an anisotropic 3D Hubbard model at half-filling

We study the 3D anisotropic Hubbard model on a cubic lattice with hopping parameter t in the x- and y-directions and a possibly different hopping parameter t_z in the z-direction; this model interpolates between the 2D and 3D Hubbard models corresponding to the limiting cases t_z=0 and t_z=t, respectively. We first derive all-order asymptotic expansions for the density of states. Using these expansions and units such that t=1, we analyze how the Néel temperature and the antiferromagnetic mean field depend on the coupling parameter, U, and on the hopping parameter t_z. We derive asymptotic formulas valid in the weak coupling regime, and we study in particular the transition from the three-dimensional to the two-dimensional model as t_z → 0. It is found that the asymptotic formulas are qualitatively different for t_z = 0 (the two-dimensional case) and t_z > 0 (the case of nonzero hopping in the z-direction). Our results show that certain universality features of the three-dimensional Hubbard model are lost in the limit t_z → 0 in which the three-dimensional model reduces to the two-dimensional model.