Two diverging length scales in the structure of jammed packings

TL;DR

This paper identifies two distinct diverging length scales in jammed packings of frictionless spheres near the jamming transition, revealing different critical behaviors in contact correlations and fluctuations.

Contribution

It uncovers and characterizes two separate diverging length scales, $\xi_{Z}$ and $\xi_{f}$, with different critical exponents, advancing understanding of the structure near jamming.

Findings

Two length scales diverge as the jamming transition is approached.

The exponents for divergence differ between the two length scales.

Contact fluctuations are suppressed below the scale $\xi_{f}$, indicating hyperuniformity.

Abstract

At densities higher than the jamming transition for athermal, frictionless repulsive spheres we find two distinct length scales, both of which diverge as a power law as the transition is approached. The first, $\xi_{Z}$, is associated with the two-point correlation function for the number of contacts on two particles as a function of the particle separation. The second, $\xi_{f}$, is associated with contact-number fluctuations in subsystems of different sizes. On scales below $\xi_{f}$ the fluctuations are highly suppressed, similar to the phenomenon of hyperuniformity usually associated with density fluctuations. The exponents for the divergence of $\xi_{Z}$ and $\xi_{f}$ are different and appear to be different in two and three dimensions.