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: $T_{\mathrm{N}}$, the Néel order-disorder transition temperature ($\propto U^{-1\mathrm{}}$ at large $U$) and a higher critical temperature $T_M$, at which the atoms lose all vestige of localized moments and at which the insulator-metal transition occurs ($T_M\propto U$ at large $U$). For $U$ less than 0.27 of the bandwidth only $T_M$ exists.