论文标题
关于SU（N）Nagaoka的铁磁敏感性的分歧
On the Divergence of the Ferromagnetic Susceptibility in the SU(N) Nagaoka-Thouless Ferromagnet
论文作者
论文摘要
使用有限温度强耦合膨胀对SU（N）Hubbard模型，我们计算了该模型的热力学特性在Indite-$ U $限制中的任意密度$ 0 \ leqρ\ leq 1 $和所有$ n $。我们表达了该模型作为居里术语的铁磁敏感性，以及$Δχ$，超过居里行为的过量敏感性。我们表明，在双方晶格上，图绘制了$Δχ$的贡献在孔密度$Δ= 1-ρ$中为零的极限。通过将所有图的贡献概括为封闭环组成的所有图表，我们发现低孔密度的铁磁敏感性指数呈$ \ exp {δ/t} $，在两个及更高尺寸中为$ t \ to $ t \至0 $。这表明Nagaoka-无效的铁磁状态是在足够低的孔密度和足够低温下的热力学状态存在的。使用SU（N）参数$ n $的常数$δ$ scales as 1/n $表示，随着铁磁订单的特征温度尺度下降，铁磁性逐渐减弱。
Using finite temperature strong coupling expansions for the SU(N) Hubbard Model, we calculate the thermodynamic properties of the model in the infinite-$U$ limit for arbitrary density $0\leq ρ\leq 1$ and all $N$. We express the ferromagnetic susceptibility of the model as a Curie term plus a $Δχ$, an excess susceptibility above the Curie-behavior. We show that, on a bipartite lattice, graph by graph the contributions to $Δχ$ are non-negative in the limit that the hole density $δ=1-ρ$ goes to zero. By summing the contributions from all graphs consisting of closed loops we find that the low hole-density ferromagnetic susceptibility diverges exponentially as $\exp{Δ/T}$ as $T \to 0$ in two and higher dimensions. This demonstrates that Nagaoka-Thouless ferromagnetic state exists as a thermodynamic state of matter at low enough density of holes and sufficiently low temperatures. The constant $Δ$ scales with the SU(N) parameter $N$ as $1/N$ implying that ferromagnetism is gradually weakened with increasing $N$ as the characteristic temperature scale for ferromagnetic order goes down.
