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