Phase separation in the large-spin {\it t}-{\it J} model

We investigate the phase diagram of the two dimensional {\it t}-{\it J} model using a recently developed technique that allows to solve the mean-field model hamiltonian with a variational calculation. The accuracy of our estimate is controlled by means of a small parameter $1/q$, analogous to the inverse spin magnitude $1/s$ employed in studying quantum spin systems. The mathematical aspects of the method and its connection with other large-spin approaches are discussed in details. In the large-$q$ limit the problem of strongly correlated electron systems turns in the minimization of a total energy functional. We have performed numerically this optimization problem on a finite but large $L\times L$ lattice. For a single hole the static small-polaron solution is stable unless for small values of $J$, where polarons of increasing sizes have lower energy. At finite doping we recover phase separation above a critical $J$ and for any electron density, showing that the Emery {\it et al.} picture represents the semiclassical behaviour of the {\it t}-{\it J} model. Quantum fluctuations are expected to be very important especially in the small $J$ -- small doping region, where phase separation may also be suppressed.