  We propose a new treatment of the Hubbard model that is based both on the
coherent-potential approximation (CPA) and the virtual-crystal approximation
(VCA). It is well known that the equilibrium found using the one-particle CPA
Green's functions does not predict an ordered magnetic ground state, while
Stoner's mean-field treatment, which is equivalent to the VCA on the Hubbard
model, does so for a wide range of parameters. A hybrid treatment, the tau-CPA,
is developed, in which a particle is assumed to be scattered from an array of
static opposite spins for a time tau related to the inverse of the band width.
The propagation is treated in the CPA over this period; thereafter the particle
sees the time-averaged effect of the scatterers and hence can be treated in the
VCA. This model, with suitable approximations, does predict magnetism for a
modified Stoner criterion.
