  We derive the random-phase approximation for spin excitations in general
multi-band Hubbard models, starting from a collinear ferromagnetic Hartree-Fock
ground state. The results are compared with those of a recently introduced
variational many-body approach to spin-waves in itinerant ferromagnets. As we
exemplify for Hubbard models with one and two bands, the two approaches lead to
qualitatively different results. The discrepancies can be traced back to the
fact that the Hartree-Fock theory fails to describe properly the local moments
which naturally arise in a correlated-electron theory.
