American Chemical Society, Journal of Physical Chemistry B (Soft Condensed Matter and Biophysical Chemistry), 42(117), p. 12979-12994, 2013
DOI: 10.1021/jp402235d
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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. ; Comment: 26 pages, 7 figures -- to be published in a Special Issue of The Journal of Physical Chemistry B in honor of Peter G. Wolynes -- paper I is arXiv:1208.0421