Spherical 2 + p spin-glass model: an exactly solvable model for glass to spin-glass transition.

We present the full phase diagram of the spherical 2 + p spin-glass model with p > or = 4. The main outcome is the presence of a phase with both properties of full replica symmetry breaking phases of discrete models, e.g., the Sherrington-Kirkpatrick model, and those of one replica symmetry breaking. This phase has a finite complexity which leads to different dynamic and static properties. The phase diagram is rich enough to allow the study of different kinds of glass to spin glass and spin glass to spin glass phase transitions.