Phase separation in the Hubbard Model
  Making use of symmetry properties and known exact results for the Hubbard Model on bipartite lattice, we show that (1) there is no phase separation for repulsive coupling at low dopings, (2) phase separation and superconductivity co-exist in the ground states for attractive coupling in a range of filling fractions. 
Chi Au, Bao-Heng Zhao, and H. T. Nieh