Constraints on collective density variables: Two dimensions

The features associated with collective density variables in two dimensions using numerical exploration techniques to generate particle patterns in the classical ground state were examined. It was shown that the particle pair interactions were governed by a continuous, bounded potential. The three structural regimes were distinguished, as the number of constrained wave vectors was increased-disordered, wavy crystalline and crystalline regimes-each with characteristics distinguishing features. It was demonstrated that the 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.