title: Exact theory of dense amorphous hard spheres in high dimension. II. The high density regime and the Gardner transition.
abstract: We consider the theory of the glass phase and jamming of hard spheres in the large space dimension limit. Building upon the exact expression for the free-energy functional obtained previously, we find that the random first order transition (RFOT) scenario is realized here with two thermodynamic transitions: the usual Kauzmann point associated with entropy crisis and a further transition at higher pressures in which a glassy structure of microstates is developed within each amorphous state. This kind of glass-glass transition into a phase dominating the higher densities was described years ago by Elisabeth Gardner, and may well be a generic feature of RFOT. Microstates that are small excitations of an amorphous matrix-separated by low entropic or energetic barriers-thus emerge naturally, and modify the high pressure (or low temperature) limit of the thermodynamic functions.
authors.affiliation: LPS, École Normale Supérieure, UMR 8550 CNRS, 24 Rue Lhomond, 75005 Paris, France.
authors.forename: Jorge
authors.initials: J
authors.lastname: Kurchan
authors.forename: Giorgio
authors.initials: G
authors.lastname: Parisi
authors.forename: Pierfrancesco
authors.initials: P
authors.lastname: Urbani
authors.forename: Francesco
authors.initials: F
authors.lastname: Zamponi