Phase separation and three-site hopping in the 2-dimensional t-J model

We study the t-J model with the inclusion of the so-called three-site term which is due to the t/U → 0 expansion of the Hubbard model. We find that this singlet pair hopping term has no qualitative effect on the structure of the pure mean field phase diagram for non-magnetic states. In accordance with experimental data on high-Tc materials and some numerical studies, we also find wide regions of phase coexistence whenever the coupling J is greater than a critical value Jc. We show that Jc varies linearly with the temperature T, going to zero at T = 0.