Hubbard Model with Inter-Site Kinetic Correlations
  We introduced the inter-site electron-electron correlation to the Hubbard III approximation. This correlation was excluded in the Hubbard III approximation and also in the equivalent coherent potential approximation. Including it brings two spin dependent effects: the bandwidth correction and the bandshift correction, which both stimulate the ferromagnetic ground state. The bandshift correction factor causes an exchange splitting between the spin-up and spin-down spectrum, and its role is similar to the exchange interaction in the classic Stoner model. The spin dependent bandwidth correction lowers the kinetic energy of electrons by decreasing the majority spin bandwidth for some electron occupations with respect to the minority spin bandwidth. In certain conditions it can lead to ferromagnetic alignment. A gain in the kinetic energy achieved in this way is the opposite extreme to the effect of a gain in potential energy due to exchange splitting. The bandshift factor is a dominant force behind the ferromagnetism. The influence of the bandwidth factor is too weak to create ferromagnetism and the only result is the correction to the classic coherent potential approximation in favor of ferromagnetism. 
Grzegorz Gorski and Jerzy Mizia