In an earlier publication  by some of us, henceforth
referred to as SHTCG, the near-equilibrium configurations
of flux lines in a Nb thin film obtained from Lorentz microscope images
 were analyzed. SHTCG argued that a sequence of
flux line configurations on the fixed pinscape resembles
the instantaneous configurations
of a classical simple liquid, with the underlying pinscape playing the role
of an effective heat bath.
This conjecture implies that in the low-density limit, the pair-correlation
function g(r) should be of the form 
The present paper aims at a more thorough understanding of how structural correlations arise from microscopic properties such as the particle interactions and potential landscape. Particular questions we address include: Under what conditions can the static configurations of an interacting system in a quenched random potential give rise to liquid-like correlations of the form Eq. (1)? How does Eq. (1) compare to a theory where the quenched nature of randomness is accounted for explicitly?
We report the results of numerical simulations and present a theory that captures the essential features observed both in experiments and in our simulations, providing thus some answers to the questions raised above. In particular our simulations show that a relation of the form Eq. (1) emerges in the limit of point-like pins, i.e. pins of small spatial extent, and for broad (e.g. exponential) pinning strength distributions. In contrast, pinscapes composed of identically strong or spatially extended pins are not well described by Eq. (1). Our theory is based on the observation that the behavior of the pair correlation function at small r is dominated by strongly pinned flux lines. In the low-density limit, the functional form of the pair correlation function therefore arises essentially from a convolution of the tails of the pinning energy distribution with the probability distribution for locating a flux line at a given position.
The paper is organized as follows. We present our model and its motivation in Section II. Section III contains details of the numerical simulations. Numerical results and their discussion are given in Section IV, while Section V is devoted to a description of the underlying theoretical picture. We conclude with a discussion and summary of our results in Section VI.