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.
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