  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.
