# Can exotic disordered "stealthy" particle configurations tolerate arbitrarily large holes?

## TL;DR

This study investigates the size limitations of large holes in disordered stealthy particle configurations, revealing they cannot tolerate arbitrarily large cavities, which influences their physical and thermodynamic properties.

## Contribution

The paper provides numerical evidence that disordered stealthy configurations in up to three dimensions have a maximum hole size, indicating a structural rigidity not present in typical disordered systems.

## Key findings

- Disordered stealthy configurations cannot have arbitrarily large holes.
- Hole probability has compact support in these systems.
- Maximum hole size varies across the first three dimensions.

## Abstract

The probability of finding a spherical cavity or "hole" of arbitrarily large size in typical disordered many-particle systems in the infinite-size limit (e.g., equilibrium liquid states) is non-zero. Such "hole" statistics are intimately linked to the physical properties of the system. Disordered "stealthy' many-particle configurations in $d$-dimensional Euclidean space $\mathbb{R}^d$ are exotic amorphous states of matter that lie between a liquid and crystal that prohibit single-scattering events for a range of wave vectors and possess no Bragg peaks [Torquato et al., Phys. Rev. X, 2015, 5, 021020]. In this paper, we provide strong numerical evidence that disordered stealthy configurations across the first three space dimensions cannot tolerate arbitrarily large holes in the infinite-system-size limit, i.e., the hole probability has compact support. This structural "rigidity" property apparently endows disordered stealthy systems with novel thermodynamic and physical properties, including desirable band-gap, optical and transport characteristics. We also determine the maximum hole size that any stealthy system can possess across the first three space dimensions.