Ideal Glass and Ideal Disk Packing in Two Dimensions

Area of Science:

• Physics
• Materials Science
• Statistical Mechanics

Background:

• The ideal glass, a theoretical state with zero configurational entropy, is unattainable via thermal processes.
• Understanding disordered systems and their properties is crucial in condensed matter physics.

Purpose of the Study:

• To develop a method for constructing ideal jammed packings of soft spheres in two dimensions.
• To investigate the properties of these ideal packings, particularly their mechanical and thermal behavior.

Main Methods:

• Developing a novel computational method to generate critically jammed packings of soft spheres.
• Analyzing the resulting structures for properties like density, moduli, and density of states.

Main Results:

• Successfully constructed two-dimensional ideal jammed packings, representing the zero temperature ideal glass.
• These packings exhibit high bulk and shear moduli, anomalously high density, and hyperuniformity.
• Disordered ideal packings, like crystalline materials, show an absence of pressure scaling in shear moduli.
• The density of states avoids low-frequency power-law scaling, and these systems melt at higher temperatures.

Conclusions:

• The presented method provides a shortcut for generating well-equilibrated glassy systems.
• This work resolves a long-standing mystery regarding the properties of ideal glasses.
• The creation of ideal packings enables a comprehensive exploration of two-dimensional jammed and glassy systems.