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In very recent work the mean field theory of the jamming transition ininfinite dimensional hard spheres models was presented. Surprisingly, thistheory predicts quantitatively numerically determined characteristics ofjamming in two and three dimensions. This is a rare and unusual finding. Herewe argue that this agreement in non-generic: only for hard sphere models ithappens that sufficiently close to jamming the effective interactions are inagreement with mean-field theory, justifying the truncation of many bodyinteractions (which is the exact protocol in infinite dimensions). Anysoftening of the bare hard sphere interactions results in effectiveinteractions that are not mean-field all the way to jamming, making thediscussed phenomenon non generic.

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