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

TL;DR

This paper develops an exact theoretical framework for dense amorphous hard spheres in high dimensions, revealing two thermodynamic transitions consistent with the RFOT scenario, including a novel glass-glass transition at high densities.

Contribution

It extends the exact free-energy functional approach to high-dimensional hard spheres, demonstrating the realization of RFOT with a new glass-glass transition within each amorphous state.

Findings

Identification of two thermodynamic transitions in high-dimensional hard spheres.

Discovery of a glass-glass transition at higher densities.

Micro-states as small excitations within amorphous structures.

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 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.