Aspects of correlation function realizability

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 equilibr...

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