Glasses (aka amorphous solids) exhibit various anomalies when compared with crystals (aka ordered solids): they display enhanced transport, activated slow dynamics across energy barriers, excess vibrational modes with respect to Debye’s theory (the so-called Boson Peak), and respond drastically to very small mechanical deformations. In this work, we identify the common, universal origin to these anomalies in a realistic, three-dimensional model of glasses. We show that in packed hard spheres, vibrations become highly correlated in space and time at a sharply defined threshold, which we call “Gardner threshold”. This work is deeply related with the last developments in the analytical theory of glasses, where the glass problem has been finally solved exactly in the artificial limit of infinite spatial dimensions. The analytical solution predicts the existence of a genuine phase transition (a Gardner phase transition) within the glass, separating the glass and the jamming transitions. In this work we, not only establish the relevance of the (remanent of the) Gardner transition for real glasses, but also characterize it using well-defined observables, including time-dependent quantities and spatial correlations, that should be experimentally measurable.

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