Some recent theoretical results on amorphous packings of hard spheres

TL;DR

This paper reviews recent theoretical results on amorphous packings of hard spheres using the replica method, providing predictions for physical properties that align well with numerical simulations and extendable to various systems.

Contribution

It offers a qualitative review of the replica method's predictions on amorphous sphere packings, including equations of state and structural properties across dimensions.

Findings

Predictions match numerical simulations in 2D and 3D.

Asymptotic results for high dimensions are within rigorous bounds.

Theory extends to mixtures and potentials with attractive interactions.

Abstract

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.