  The ground state phase diagram of the extended Hubbard model containing
nearest and next-to-nearest neighbor interactions is investigated in the
thermodynamic limit using an exact method. It is found that taking into account
local correlations and adding next-to-nearest neighbor interactions both have
significant effects on the position of the phase boundaries. Improved stability
domains for the $\eta$-pairing state and for the fully saturated ferromagnetic
state at half filling have been constructed. The results show that these states
are the ground states for model Hamiltonians with realistic values of the
interaction parameters.
