Magnetism in Single-Band Models Exact One-Dimensional Wave Functions Generalised to Higher Dimensions

States of complete spin-alignment, except for one reversed spin, are investigated for a Fermi gas with 0'-function interactions and for the Hubbard model. A variational ansatz for the wave function of such states is given and is shown to be exact in one dimension. The wave function contains a set of one-electron orbitals which satisfy certain self-consistent field equations. The wave function forms the basis of a numerical scheme, described elsewhere, which should determine whether the state of complete spin alignment in the two-dimensional Hubbard model is ever stable against spin reversal in the thermodynamic limit.