半填充各向异性3D Hubbard模型中平均场反铁磁序的普适性
Universality of mean-field antiferromagnetic order in an anisotropic 3D Hubbard model at half-filling
AI总结：
研究了立方晶格上3D各向异性Hubbard模型在半填充下的反铁磁平均场序，推导了态密度全阶渐近展开，发现三维模型的普适性特征在$t_z \ o 0$退化为二维时丧失。
摘要：
我们研究立方晶格上的3D各向异性Hubbard模型，其x和y方向的跃迁参数为$t$，z方向的跃迁参数$t_z$可能不同；该模型在极限情况$t_z=0$和$t_z=t$下分别对应2D和3D Hubbard模型。我们首先推导了态密度的全阶渐近展开。利用这些展开并采用$t=1$的单位制，我们分析了Néel温度和反铁磁平均场如何依赖于耦合参数$U$及跃迁参数$t_z$。我们推导了在弱耦合区域有效的渐近公式，并特别研究了当$t_z \ o 0$时从三维模型到二维模型的转变。研究发现，对于$t_z = 0$（二维情况）和$t_z > 0$（z方向跃迁非零的情况），渐近公式存在定性差异。结果表明，三维Hubbard模型的某些普适性特征在$t_z \ o 0$的极限下（即三维模型退化为二维模型时）会丧失。
英文摘要：
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.
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