Glass-Glass Transition and New Dynamical Singularity Points in an Analytically Solvable $p$-Spin Glasslike Model

We introduce and analytically study a generalized p-spin glasslike model that captures some of the main features of attractive glasses, recently found by mode coupling investigations, such as a glass-glass transition line and dynamical singularity points characterized by a logarithmic time dependence of the relaxation. The model also displays features not predicted by the mode coupling scenario that could further describe the attractive glasses behavior, such as aging effects with new dynamical singularity points ruled by logarithmic laws or the presence of a glass spinodal line.