Determining pair interactions from structural correlations

We examine metastable configurations of a two-dimensional system of interac ting particles on a quenched random potential landscape and ask how the con figurational pair correlation function is related to the particle interacti ons and the statistical properties of the potential landscape. Understandin g this relation facilitates quantitative studies of magnetic flux-line inte ractions in type-ii superconductors, using structural information available from Lorentz microscope images or Bitter decorations. Previous work by som e of us supported the conjecture that the relationship between pair correla tions and interactions in pinned flux-line ensembles is analogous to the co rresponding relationship in the theory of simple liquids. The present paper aims at a more thorough understanding of this relation. We report the resu lts of numerical simulations and present a theory for the low-density behav ior of the pair-correlation function, which agrees well with our simulation s and captures features observed in experiments. In particular, we find tha t the resulting description goes beyond the conjectured classical liquid-ty pe relation and we remark on the differences. [S0163-1829(98)02446-1].