The Ideal Glass and the Ideal Disk Packing in Two Dimensions

TL;DR

This paper introduces a method to construct ideal jammed packings of soft spheres in two dimensions, revealing unique mechanical and structural properties of the ideal glass that advance understanding of disordered systems.

Contribution

The authors present a novel approach to generate zero-temperature ideal glass packings in 2D, enabling detailed study of their unique properties and behaviors.

Findings

Critically jammed packings exhibit high bulk and shear moduli.

Disordered ideal packings lack pressure scaling in shear moduli.

Configurations display hyperuniformity and melt at high temperatures.

Abstract

The ideal glass, a disordered system of particles with zero configurational entropy, cannot be realized through thermal processes. Nevertheless, we present a method for constructing ideal jammed packings of soft spheres, and thus the zero temperature ideal glass, in two dimensions. In line with the predicted properties, these critically jammed packings have high bulk and shear moduli as well as an anomalously high density. While the absence of pressure scaling in the shear moduli of crystalline materials is often attributed to the ordered nature of the particles, we show for the first time that disordered ideal packings also have this feature. We also find that the density of states avoids the low frequency power law scaling famously found in most amorphous materials, these configurations display hyperuniformity, and they melt at unusually high temperatures as compared to conventional packings. In addition to resolving a long-standing mystery, this methodology represents a valuable shortcut in the generation of well-equilibrated glassy systems. The creation of such an ideal packing makes possible a complete exploration and explanation of two dimensional jammed and glassy systems.