  To understand the interplay of d-wave superconductivity and
antiferromagnetism in the cuprates, we consider a two-dimensional extended
Hubbard model with nearest neighbor attractive interaction. Free energy of the
homogeneous (coexisting superconducting and antiferromagnetic) state calculated
a s a function of the band filling shows a region of of phase separation. The
phase separation caused by the intersite attractive force leads to novel
insights into salient features of the pseudogap phase diagram. In particular,
the upper crossover curve can be identified with the phase separation boundary.
At zero temperature, the boundary constitutes a critical point. The
inhomogeneity observed in the underdoped cuprates is a consequence of
incomplete phase separation. The disorder (inhomogeneity) brings about the
disparity between the high pseudogap temperature and the low bulk
superconducting transition temperature.
