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Using finite temperature strong coupling expansions for the SU(N) HubbardModel, we calculate the thermodynamic properties of the model in theinfinite-$U$ limit for arbitrary density $0\leq \rho \leq 1$ and all $N$. Weexpress the ferromagnetic susceptibility of the model as a Curie term plus a$\Delta \chi$, an excess susceptibility above the Curie-behavior. We show that,on a bipartite lattice, graph by graph the contributions to $\Delta \chi$ arenon-negative in the limit that the hole density $\delta=1-\rho$ goes to zero.By summing the contributions from all graphs consisting of closed loops we findthat the low hole-density ferromagnetic susceptibility diverges exponentiallyas $\exp{\Delta /T}$ as $T \to 0$ in two and higher dimensions. Thisdemonstrates that Nagaoka-Thouless ferromagnetic state exists as athermodynamic state of matter at low enough density of holes and sufficientlylow temperatures. The constant $\Delta$ scales with the SU(N) parameter $N$ as$1/N$ implying that ferromagnetism is gradually weakened with increasing $N$ asthe characteristic temperature scale for ferromagnetic order goes down.

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