The Ideal Glass and the Ideal Disk Packing in Two Dimensions

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. Finally, these configurations display hyperuniformity. 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. :contentReference[oaicite:0]{index=0}

Publication Details

• Authors: Viola Bolton-Lum, R. Cameron Dennis, Peter Morse, Eric Corwin
• Journal: arXiv Preprint
• ArXiv ID: 2404.07492
• Publication Date: April 11, 2024
• DOI: 10.48550/arXiv.2404.07492

Key Findings

• Construction of Ideal Jammed Packings: Developed a method to create two-dimensional ideal jammed packings of soft spheres, representing the zero-temperature ideal glass.
• Mechanical Properties: These packings exhibit high bulk and shear moduli and an anomalously high density, aligning with predicted properties of ideal glasses.
• Pressure Scaling in Shear Moduli: Demonstrated that disordered ideal packings, like their crystalline counterparts, lack pressure scaling in shear moduli.
• Density of States: Identified that the density of states in these packings avoids the low-frequency power-law scaling commonly observed in amorphous materials.
• Hyperuniformity: Confirmed that the constructed configurations display hyperuniformity, indicating uniform distribution at large scales.

This study introduces a novel approach to generating two-dimensional ideal glasses, providing a framework for exploring the properties of jammed and glassy systems in disordered configurations.