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

TL;DR

This paper examines the surprising agreement between mean field theory predictions and actual jamming behavior in finite-dimensional hard sphere models, arguing that this agreement is specific to hard spheres and not a general feature.

Contribution

It demonstrates that the mean field theory's accurate predictions near jamming are specific to hard sphere models and do not extend to models with softened interactions, highlighting the non-generic nature.

Findings

Mean field theory accurately predicts jamming in hard sphere models in finite dimensions.

Softening interactions leads to deviations from mean-field predictions near jamming.

The agreement observed is specific to hard spheres and not a universal feature.

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.