  The Kondo lattice Hamiltonian with ferromagnetic Hund's coupling as a model
for manganites is investigated. The classical limit for the spin of the
(localized) $t_{2g}$ electrons is analyzed on lattices of dimension 1,2,3 and
$\infty$ using several numerical methods. The phase diagram at low temperature
is presented. A regime is identified where phase separation occurs between hole
undoped antiferromagnetic and hole-rich ferromagnetic regions. Experimental
consequences of this novel regime are discussed. Regions of incommensurate spin
correlations have also been found. Estimations of the critical temperature in
3D are compatible with experiments.
