# Hyperuniformity and generalized fluctuations at Jamming

## TL;DR

This paper investigates hyperuniformity in jammed solids, revealing that density fluctuations are only suppressed up to a finite lengthscale in the rigid phase, and hyperuniformity is absent in the jammed state.

## Contribution

It demonstrates that hyperuniformity is not a generic feature of jammed solids and explores the contrasting suppression of geometrical fluctuations.

## Key findings

- Density fluctuations are suppressed only up to a finite lengthscale in the rigid phase.
- The lengthscale of density fluctuation suppression diverges at the rigidity transition.
- Geometrical fluctuations are suppressed over a larger lengthscale than density fluctuations.

## Abstract

The suppression of density fluctuations at different length scales is the hallmark of hyperuniformity. However, its existence and significance in jammed solids is still a matter of debate. We explore the presence of this hidden order in a manybody interacting model known to exhibit a rigidity transition, and find that in contrary to exisiting speculations, density fluctuations in the rigid phase are only suppressed up to a finite lengthscale. This length scale grows and diverges at the critical point of the rigidity transition, such that the system is hyperuniform in the fluid phase. This suggests that hyperuniformity is a feature generically absent in jammed solids. Surprisingly, corresponding fluctuations in geometrical properties of the model are found to be strongly suppressed over an even greater but still finite lengthscale, indicating that the system self organizes in preference to suppress geometrical fluctuations at the expense of incurring density fluctuations.