Exact theory of dense amorphous hard spheres in high dimension. II. The high density regime and the Gardner transition

Jorge Kurchan 1, Giorgio Parisi 2, Pierfrancesco Urbani 3, Francesco Zamponi 4

The Journal of Physical Chemistry B 117 (2013) 12979-12994

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 micro-states 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. Micro states 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.

  • 1 : Physique et mécanique des milieux hétérogenes (PMMH)
    CNRS : UMR7636 – Université Pierre et Marie Curie (UPMC) - Paris VI – Université Paris VII - Paris Diderot – ESPCI ParisTech
  • 2 : Dipartimento di Fisica and INFM
    Università degli studi di Roma I - La Sapienza
  • 3 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 4 : Laboratoire de Physique Théorique de l'ENS (LPTENS)
    CNRS : UMR8549 – Université Pierre et Marie Curie (UPMC) - Paris VI – École normale supérieure [ENS] - Paris