Constraints on collective density variables: Two dimensions

Collective density variables (k) have proved to be useful tools in the study of many-body problems in a variety of fields that are concerned with structural and kinematic phenomena. In spite of their broad applicability, mathematical understanding of collective density variables remains an underexplored subject. In this paper, we examine features associated with collective density variables in two dimensions using numerical exploration techniques to generate particle patterns in the classical ground state. Particle pair interactions are governed by a continuous, bounded potential. Our approach involves constraining related collective parameters C (k), with wave vector k magnitudes at or below a chosen cutoff, to their absolute minimum values. Density fluctuations for those k's thus are suppressed. The resulting investigation distinguishes three structural regimes as the number of constrained wave vectors is increased---disordered, wavy crystalline, and crystalline regimes---each with characteristic distinguishing features. It should be noted that our choice of pair potential can lead to pair correlation functions that exhibit an effective hard core and thus signal the formation of a hard-disk-like equilibrium fluid. In addition, our method creates particle patterns that are hyperuniform, thus supporting the notion that structural glasses can be hyperuniform as the temperature T0.