  The phase diagram of the simplest approximation to Double-Exchange systems,
the bosonic Double-Exchange model with antiferromagnetic super-exchange
coupling, is fully worked out by means of Monte Carlo simulations, large-N
expansions and Variational Mean-Field calculations. We find a rich phase
diagram, with no first-order phase transitions. The most surprising finding is
the existence of a segment like ordered phase at low temperature for
intermediate AFM coupling which cannot be detected in neutron-scattering
experiments. This is signaled by a maximum (a cusp) in the specific heat. Below
the phase-transition, only short-range ordering would be found in
neutron-scattering. Researchers looking for a Quantum Critical Point in
manganites should be wary of this possibility. Finite-Size Scaling estimates of
critical exponents are presented, although large scaling corrections are
present in the reachable lattice sizes.
