  The spherical mean field approximation of a spin-1 model with p-body quenched
disordered interaction is investigated. Depending on temperature and chemical
potential the system is found in a paramagnetic or in a glassy phase and the
transition between these phases can be of different nature. In given conditions
inverse freezing occurs. As $p=2$ the glassy phase is replica symmetric and the
transition is always continuous in the phase diagram. For $p>2$ the exact
solution for the glassy phase is obtained by the one step replica symmetry
breaking Ansatz. Different scenarios arise for both the dynamic and the
thermodynamic transitions. These include (i) the usual random first order
transition (Kauzmann-like) preceded by a dynamic transition, typical of
mean-field glasses, (ii) a thermodynamic first order transition with phase
coexistence and latent heat and (iii) a regime of inversion of static and
dynamic transition lines. In the latter case a thermodynamic stable glassy
phase, with zero configurational entropy, is dynamically accessible from the
paramagnetic phase. Crossover between different transition regimes are analyzed
by means of Replica Symmetry Breaking theory and a detailed study of the
complexity and of the stability of the static solution is performed throughout
the space of external thermodynamic parameters.
