Exotic Ground States of Directional Pair Potentials via Collective-Density Variables

Abstract

Collective-density variables have proved to be a useful tool in the prediction and manipulation of how spatial patterns form in the classical many-body problem. Previous work has employed properties of collective-density variables along with a robust numerical optimization technique to find the classical ground states of many-particle systems subject to radial pair potentials in one, two and three dimensions. That work led to the identification of ordered and disordered classical ground states. In this paper, we extend these collective-coordinate studies by investigating the ground states of directional pair potentials in two dimensions. Our study focuses on directional potentials whose Fourier representations are non-zero on compact sets that are symmetric with respect to the origin and zero everywhere else. We choose to focus on one representative set which has exotic ground-state properties: two circles whose centers are separated by some fixed distance. We obtain ground states for this "two-circle" potential that display large void regions in the disordered regime. As more degrees of freedom are constrained the ground states exhibit a collapse of dimensionality characterized by the emergence of filamentary structures and linear chains. This collapse of dimensionality has not been observed before in related studies.

21 pages, 11 figures

References in corpus (8)

• Classical Disordered Ground States: Super-Ideal Gases, and Stealth and Equi-Luminous Materials
• Effects of patch size and number within a simple model of patchy colloids
• Point processes in arbitrary dimension from fermionic gases, random matrix theory, and number theory
• Crystalline ground states for classical particles
• Gaussian core model phase diagram and pair correlations in high Euclidean dimensions
• New Duality Relations for Classical Ground States
• From bcc to fcc: interplay between oscillating long-range and repulsive short-range forces
• Inherent Structures for Soft Long-Range Interactions in Two-Dimensional Many-Particle Systems

Cited by in corpus (6)

• Hyperuniform States of Matter
• Hyperuniformity and its Generalizations
• Ensemble Theory for Stealthy Hyperuniform Disordered Ground States
• Ground states of stealthy hyperuniform potentials: I. Entropically favored configurations
• Generating large disordered stealthy hyperuniform systems with ultra-high accuracy to determine their physical properties
• Hyperuniformity Order Metric of Barlow Packings