The mixed p-spin model: selecting, following and losing states

Differently to crystals, amorphous materials can preserve the memory of their past and their thermodynamic properties are directly connected to the protocol used to prepare them (think of ordinary glasses). In this thesis, I present an abstract model of glass for which many analytical results are already known: the p-spin spherical model (introduced 30 years ago). In particular, I focus the attention on a particular preparation protocol: the system is equilibrated at one temperature T’ and instantaneously cooled to a second temperature T. If choosing an opportunely tuned "mixed" p-spin model, the aforementioned protocol shows a phenomenology analogous to that of real glass. The system presents final properties that strictly depend on the first temperature T’, thus preserving the memory of the initial condition. This is the first analytically solvable model which presents such a dependence, and it is expected to bring new insights into the theoretical understanding of amorphous material.