  We report on a non-equilibrium phase of matter, the minimally disordered
crystal phase, which we find exists between the maximally amorphous glasses and
the ideal crystal. Even though these near crystals appear highly ordered, they
display glassy and jamming features akin to those observed in amorphous solids.
Structurally, they exhibit a power-law scaling in their probability
distribution of weak forces and small interparticle gaps as well as a flat
density of vibrational states. Dynamically, they display anomalous aging above
a characteristic pressure. Quantitatively this disordered crystal phase has
much in common with the Gardner-like phase seen in maximally disordered solids.
Near crystals should be amenable to experimental realizations in
commercially-available particulate systems and are to be indispensable in
verifying the theory of amorphous materials.
