The Hubbard model including nearest neighbor interaction is studied at
T=0 on a d-dimensional hypercubic lattice (d much greater than 1) clo
se to half filling. For the model in d=infinity we derive the exact re
sult that the ground state at weak coupling is phase separated. Result
s for lower dimensions are then derived in a 1/d expansion. To obtain
these results we first consider possible second order transitions. One
then finds that the broken-symmetry phase near half filling is incomm
ensurate. However, the corresponding ground state has negative compres
sibly and is hence thermodynamically unstable. A Maxwell construction
is used to construct the actual phase separated ground state, which co
nsists of homogeneous lower-density and antiferromagnetic or charge de
nsity wave higher-density regions. It is shown that both the doping le
vel below which phase separation occurs and the order parameter differ
from the corresponding Hartree results by a renormalization factor q
of order unity. This renormalization factor q is calculated systematic
ally up to O(1/D) in a 1/d expansion and turns out to be identical to
the renormalization factor previously calculated for the low-temperatu
re thermodynamics at half filling.