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

Abstract

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 $t_z\to 0$. 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 $t_z\to 0$ in which the three-dimensional model reduces to the two-dimensional model.

arXiv comment39 pages, 9 figures

References in corpus (8)

• The Hubbard Model
• Generalized Hartree-Fock Theory and the Hubbard Model
• Critical Temperature and Energy Gap for the BCS Equation
• Thermodynamics and magnetism in the 2D-3D crossover of the Hubbard model
• Phase diagrams of the 2D t-t'-U Hubbard model from an extended mean field method
• The BCS Energy Gap at High Density
• Universal and nonuniversal features of Bardeen-Cooper-Schrieffer theory with finite-range interactions
• Asymptotic analysis of Dotsenko-Fateev integrals

Cited by in corpus (1)

• Update of Hartree--Fock theory for Hubbard-like models