Limits on phase separation for two-dimensional strongly correlated electrons

From calculations of the high-temperature series for the free energy of the two-dimensional t-J model we construct a series for ratios of the free energy per hole. The ratios can be extrapolated very accurately to low temperatures and used to investigate phase separation. Our results confirm that phase separation occurs only for J/t greater than or equal to 1.2. Also, the phase transition into the phase-separated state has T-c approximate to 0.25J for large J/t.