Existence of Two Phase Transitions in Hubbard Model

We solve the Bubbard model, for one electron per atom in a simple cubic structure, using one-particle Green's functions. We determine the accuracy of this calculation to be good by comparison with an exact solution by Lieb and Wu of a one-dimensional limiting case. When the Coulomb interaction U exceeds about 0.27 of the bandwidth in three dimensions we find there are two critical temperatures: TN, the N\'eel order-disorder transition temperature (∝U^-1 at large U) and a higher critical temperature TM, at which the atoms lose all vestige of localized moments and at which the insulator-metal transition occurs (TM∝U at large U). For U less than 0.27 of the bandwidth only TM exists.