  We analyze the Blume-Emery-Griffiths model with disordered magnetic
interaction that displays the inverse freezing phenomenon. The behavior of this
spin-1 model in crystal field is studied throughout the phase diagram and the
transition and spinodal lines for the model are computed using the Full Replica
Symmetry Breaking Ansatz that always yields a thermodynamically stable phase.
We compare the results both with the formulation of the same model in terms of
Ising spins on lattice gas, where no reentrance takes place, and with the model
with generalized spin variables recently introduced by Schupper and Shnerb
[Phys. Rev. Lett. {\bf 93} 037202 (2004)], for which the reentrance is enhanced
as the ratio between the degeneracy of full to empty sites increases. The
simplest version of all these models, known as the Ghatak-Sherrington model,
turns out to hold all the general features characterizing an inverse transition
to an amorphous phase, including the right thermodynamic behavior.
