  A novel form of amorphous matter characterized by marginal stability was
recently discovered in the mean-field theory of structural glasses. Using this
approach, we provide complete phase diagrams delimiting the location of the
marginally stable glass phase for a large variety of pair interactions and
physical conditions, extensively exploring physical regimes relevant to
granular matter, foams, emulsions, hard and soft colloids, and molecular
glasses. We find that all types of glasses may become marginally stable, but
the extent of the marginally stable phase highly depends on the preparation
protocol. Our results suggest that marginal phases should be observable for
colloidal and non-Brownian particles near jamming, and poorly annealed glasses.
For well-annealed glasses, two distinct marginal phases are predicted. Our
study unifies previous results on marginal stability in mean-field models, and
will be useful to guide numerical simulations and experiments aimed at
detecting marginal stability in finite dimensional amorphous materials.
