Reply to Morse and Charbonneau on "Explicit analytical solution for random close packing in $d=2$ and $d=3$"

TL;DR

This paper discusses the limitations of an analytical solution for random close packing in high dimensions, emphasizing its success in lower dimensions and the theoretical challenges in larger ones, while reaffirming its physical relevance.

Contribution

It argues that existing analytical solutions based on contact numbers are unlikely to work in high dimensions, but highlights the significance of a simple statistical solution in lower dimensions.

Findings

The solution aligns well with data in dimensions less than 6.

Deviations occur for dimensions 6 and above due to geometric constraints.

The analytical approach captures key physics in 2 to 5 dimensions.

Abstract

A Comment by Morse and Charbonneau shows that our recent analytical solution to the random close packing (RCP) problem is in good agreement with packings data in dimensions $d<6$ but deviates from the data for $d\geq6$. In this Reply we argue, using results related to the $E_{8}$ Lie group, that no RCP solution based on contact numbers and marginal stability is expected to capture RCP in large space dimensions $d \geq 8$ where a large gap exists between nearest neighbours already at $d=8$. The fact remains that the result in [A. Zaccone, Phys. Rev. Lett. 128, 028002 (2022)] is currently the only simple analytical solution to the RCP problem based on statistical arguments, which captures a good deal of the underlying physics in $d=2,3,4,5$.