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

Abstract

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 ≤ ρ ≤ 1 and all N . We express the ferromagnetic susceptibility of the model as a Curie term plus a ∆χ, an excess susceptibility above the Curie-behavior. We show that, on a bipartite lattice, graph by graph the contributions to ∆χ 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 ∆/T as T → 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 ∆ 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.