Determining pair interactions from structural correlations

We examine metastable configurations of a two-dimensional system of interacting particles on a quenched random potential landscape and ask how the configurational pair correlation function is related to the particle interactions and the statistical properties of the potential landscape. Understanding this relation facilitates quantitative studies of magnetic flux-line interactions in type-II superconductors, using structural information available from Lorentz microscope images or Bitter decorations. Previous work by some of us supported the conjecture that the relationship between pair correlations and interactions in pinned flux-line ensembles is analogous to the corresponding relationship in the theory of simple liquids. The present paper aims at a more thorough understanding of this relation. We report the results of numerical simulations and present a theory for the low-density behavior of the pair-correlation function, which agrees well with our simulations and captures features observed in experiments. In particular, we find that the resulting description goes beyond the conjectured classical liquid-type relation and we remark on the differences.