  Hyperuniformity characterizes a state of matter that is poised at a critical
point at which density or volume-fraction fluctuations are anomalously
suppressed at infinite wavelengths. Recently, much attention has been given to
the link between strict jamming and hyperuniformity in frictionless
hard-particle packings. Doing so requires one to study very large packings,
which can be difficult to jam properly. We modify the rigorous linear
programming method of Donev et al. [J. Comp. Phys. 197, 139 (2004)] in order to
test for jamming in putatively jammed packings of hard-disks in two dimensions.
We find that various standard packing protocols struggle to reliably create
packings that are jammed for even modest system sizes; importantly, these
packings appear to be jammed by conventional tests. We present evidence that
suggests that deviations from hyperuniformity in putative maximally random
jammed (MRJ) packings can in part be explained by a shortcoming in generating
exactly-jammed configurations due to a type of "critical slowing down" as the
necessary rearrangements become difficult to realize by numerical protocols.
Additionally, various protocols are able to produce packings exhibiting
hyperuniformity to different extents, but this is because certain protocols are
better able to approach exactly-jammed configurations. Nonetheless, while one
should not generally expect exact hyperuniformity for disordered packings with
rattlers, we find that when jamming is ensured, our packings are very nearly
hyperuniform, and deviations from hyperuniformity correlate with an inability
to ensure jamming, suggesting that strict jamming and hyperuniformity are
indeed linked. This raises the possibility that the ideal MRJ packings have no
rattlers. Our work provides the impetus for the development of packing
algorithms that produce large disordered strictly jammed packings that are
rattler-free.
