Aspects of correlation function realizability

Abstract

The pair-correlation function g2(r) describes short-range order in many-particle systems. It must obey two necessary conditions: (i) non-negativity for all distances r, and (ii) non-negativity of its associated structure factor S(k) for all k. For the elementary unit step-function g2 form, previous work [F. H. Stillinger, S. Torquato, J. M. Eroles, and T. M. Truskett, J. Phys. Chem. B 105, 6592 (2001)] indicates that (i) and (ii) could be formally satisfied, but only up to a terminal density at which the covering fraction of particle exclusion diameters equaled 2−d in d dimensions. To test whether the unit step g2 is actually achievable in many-particle systems up to the apparent terminal density, a stochastic optimization procedure has been used to shift particles in large test systems toward this target g2. Numerical calculations for d=1 and 2 confirm that the step function g2 is indeed realizable up to the terminal density, but with substantial deviation from the configurational preferences of equilibrium hard-rod and hard-disk models. We show that lineal statistical measures are particularly sensitive to this difference. Our results also illustrate the characteristics of “closest approach” to the step function g2 above the terminal density.