Ground states of stealthy hyperuniform potentials: I. Entropically favored configurations

TL;DR

This study investigates the structure and properties of disordered hyperuniform ground states in stealthy potentials, using molecular dynamics simulations to verify theoretical predictions and explore phase transitions at varying densities.

Contribution

The paper introduces a detailed simulation approach to sample stealthy hyperuniform ground states and extends understanding of their structural behavior across different densities.

Findings

High-density disordered states behave like 'pseudo' disordered hard-sphere systems.

Decreasing density leads to increased short-range order and a transition to crystalline states.

Different stealthy potentials yield similar ground-state ensembles in the zero-temperature limit.

Abstract

Systems of particles interacting with "stealthy" pair potentials have been shown to possess infinitely degenerate disordered hyperuniform classical ground states with novel physical properties. Previous attempts to sample the infinitely degenerate ground states used energy minimization techniques, introducing algorithmic dependence that is artificial in nature. Recently, an ensemble theory of stealthy hyperuniform ground states was formulated to predict the structure and thermodynamics that was shown to be in excellent agreement with corresponding computer simulation results in the canonical ensemble (in the zero-temperature limit). In this paper, we provide details and justifications of the simulation procedure, which involves performing molecular dynamics simulations at sufficiently low temperatures and minimizing the energy of the snapshots for both the high-density disordered regime, where the theory applies, as well as lower densities. We also use numerical simulations to extend our study to the lower-density regime. We report results for the pair correlation functions, structure factors, and Voronoi cell statistics. In the high-density regime, we verify the theoretical ansatz that stealthy disordered ground states behave like "pseudo" disordered equilibrium hard-sphere systems in Fourier space. These results show that as the density decreases from the high-density limit, the disordered ground states in the canonical ensemble are characterized by an increasing degree of short-range order and eventually the system undergoes a phase transition to crystalline ground states. We also provide numerical evidence suggesting that different forms of stealthy pair potentials produce the same ground-state ensemble in the zero-temperature limit. Our techniques may be applied to sample this limit of the canonical ensemble of other potentials with highly degenerate ground states.