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On the Divergence of the Ferromagnetic Susceptibility in the SU(N) Nagaoka-Thouless Ferromagnet

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.