How Generic are the Robust Theoretical Aspects of Jamming in Hard Sphere Models?

Abstract

In very recent work the mean field theory of the jamming transition in infinite dimensional hard spheres models was presented. Surprisingly, this theory predicts quantitatively numerically determined characteristics of jamming in two and three dimensions. This is a rare and unusual finding. Here we argue that this agreement in non-generic: only for hard sphere models it happens that sufficiently close to jamming the effective interactions are in agreement with mean-field theory, justifying the truncation of many body interactions (which is the exact protocol in infinite dimensions). Any softening of the bare hard sphere interactions results in effective interactions that are not mean-field all the way to jamming, making the discussed phenomenon non generic.

Supplementary Material added. Keywords: Amorphous, Soft Matter, force\-law, hard spheres, soft spheres, jamming, colloids, simulation, Emergent interactions

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• Mean-Field Predictions of Scaling Prefactors Match Low-Dimensional Jammed Packings
• Instabilities of Time-averaged Configurations in Thermal Glasses
• Effective Forces in Thermal Amorphous Solids with Generic Interactions
• Jamming is a first-order transition with quenched disorder in amorphous materials sheared by cyclic quasistatic deformations