Some recent theoretical results on amorphous packings of hard spheres

The aim of this paper is to review and discuss qualitatively some results on the properties of amorphous packings of hard spheres that were recently obtained by means of the replica method. The theory gives predictions for the equation of state of the glass, the complexity of the metastable states, the scaling of the pressure close to jamming, the coordination of the packing and the pair correlation function in any space dimension d. The predictions compare very well with numerical simulations in d=3 and somehow also in d=2. The asymptotic predictions for d->oo are within the rigorous bounds. The theory can be extended to binary mixtures and to hard core potentials with an attractive tail or square well.Comment: 7 pages, 6 figures; proceedings of the X International Workshop on Disordered Systems, Molveno (TN), Italy, March 200

The ideal glass transition of Hard Spheres

We use the replica method to study the ideal glass transition of a liquid of identical Hard Spheres. We obtain estimates of the configurational entropy in the liquid phase, of the Kauzmann packing fraction, in the range 0.58--0.62, and of the random close packing density, in the range 0.64--0.67, depending on the approximation we use for the equation of state of the liquid. We also compute the pair correlation function in the glassy states (i.e., dense amorphous packings) and we find that the mean coordination number at random close packing is equal to 6. All these results compare well with numerical simulations and with other existing theories.Comment: 13 pages, 8 figure