Inverse-degeneracy expansions for the Hubbard model

The statistical mechanics of itinerant-electron magnets, such as the transition metals, depends on the number of bands. A ν-band Hubbard model is used to describe this. It is shown that Stoner theory is exact in the large-ν limit. For intermediate ν, a classical (nonquantum) spin model (the static approximation) is appropriate. For small ν, a quantum description of the magnetization is necessary. Two expansions about the large-ν limit are developed. In the first, useful in the ferromagnetic region, one recovers the Stoner random-phase approximation theory as the leading two terms. In the other, useful in both the paramagnetic and ferromagnetic regions, the leading term is the static approximation and the leading correction includes quantum fluctuations. This correction increases the specific heat. It also provides for an approximate Bose-type function for nonlinear spin fluctuations.