Abstract We study Hartree–Fock theory at half-filling for 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
tz t z in the z -direction; this model interpolates between the 2D and 3D Hubbard models corresponding to the limiting cases
tz=0 t z = 0 and
tz=t 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 t = 1 , we analyze how the Néel temperature and the antiferromagnetic mean field depend on the coupling parameter, U , and on the hopping parameter
tz 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
tz→0 t z → 0 . It is found that the asymptotic formulas are qualitatively different for
tz=0 t z = 0 (the two-dimensional case) and
tz>0 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
tz→0 t z → 0 in which the three-dimensional model reduces to the two-dimensional model.
We show that the Onsager-field theory for itinerant systems is also quite useful for arbitrary filling of the two-dimensional (2D) and 3D Hubbard models in the weak to intermediate coupling of
U, yielding various magnetic properties in agreement with the results of quantum Monte Carlo simulations and the two-particle self-consistent method of Vilk et al. Any small doping into the antiferromagnetic ground state of the half-filled 3D model introduces an incommensurate phase with a significant reduction due to fluctuations.
We have investigated the antiferromagnetic phase of two-dimensional (2D), three-dimensional (3D), and extended Hubbard models on a bipartite cubic lattice by means of the composite operator method within a two-pole approximation. This approach yields a fully self-consistent treatment of the antiferromagnetic state that respects the symmetry properties of both the model and the algebra. The complete phase diagram, as regards the antiferromagnetic and paramagnetic phases, has been drawn. We first reported, within a pole approximation, three kinds of transitions at half-filling: Mott-Hubbard, Mott-Heisenberg, and Heisenberg transitions. We have also found a metal-insulator transition, driven by doping, within the antiferromagnetic phase. This latter is restricted to a very small region near half-filling, and has, in contrast to what has been found by similar approaches, a finite critical Coulomb interaction as a lower bound at half-filling. Finally, it is worth noting that our antiferromagnetic gap has two independent components: one due to the antiferromagnetic correlations, and another coming from the Mott-Hubbard mechanism.
We investigate numerically the magnetic properties of the 3D Isotropic and Anisotropic Hubbard model at half-filling. The behavior of the transition temperature as a function of the anisotropic hopping parameter is qualitatively described. In the Isotropic model we measure the scaling properties of the susceptibility finding agreement with the magnetic critical exponents of the 3D Heisenberg model. We also describe several particularities concerning the implementation of our simulation in a cluster of personal computers. 1 1
We investigate numerically the magnetic properties of the 3D Isotropic and Anisotropic Hubbard model at half-filling. The behavior of the transition temperature as a function of the anisotropic hopping parameter is qualitatively described. In the Isotropic model we measure the scaling properties of the susceptibility finding agreement with the magnetic critical exponents of the 3D Heisenberg model. We also describe several particularities concerning the implementation of our simulation in a cluster of personal computers.
Magnetic properties of the half-filled Hubbard model on three-dimensional bipartite lattices have been studied by using the linked-cluster series expansion method. The series for the free energy and the staggered susceptibility have been calculated as a function of \ensuremath{\mathrm{B}}t for three-dimensional bipartite lattices for an arbitrary value of the Coulomb interaction U. We obtain a transition from a paramagnetic to an antiferromagnetic U/t-
TN /t phase diagram from the divergence of the staggered susceptibility series. Comparisons with Monte Carlo simulation, Onsager reaction field result of an effective spin Hamiltonian, and large-U Heisenberg high-temperature solutions are made.