We have shown that the pair correlation function arising from stable configurations of interacting particles in a random pinscape can contain information about both the particle interactions and also the statistical properties of the underlying pinscape. Our analysis shows that this is the case in the regime where the pinning and pair interactions are of comparable strength. If the pinning completely dominates pair interactions, the pair correlation function will essentially reveal the spatial disorder of the active pinning sites. In the opposite limit, in which the pair interactions dominate, the pair correlation function will contain features corresponding to crystalline order. In both cases, little information can be extracted about the form of the interactions.

We have derived an expression for the pair correlation
function in the limit of point-like disorder and
low flux line density, Eq. (15).
Our
theory shows that the small *r* behavior of the pair
correlation function depends both on the pair
interaction and also on the availability of
sufficiently strong pinning sites.
We found that the distribution of the latter is not necessarily
the same as the distribution of *a priori* available
pinning sites.
Rather, the dynamics favor strong pins.
Inspection of the stable configurations revealed
that the distribution of dynamically selected pins is consistent
with a process of choosing the strongest out of *n*
available pins.
For the parameters used in our
simulations, *n* = 2 described the dynamically selected
pinning strength distributions very well.
We expect however that the parameter *n*, while apparently
independent of the width of the pinning strength distribution,
should depend on both the concentration of pins and also the penetration
depth of the flux line interaction.
A more detailed investigation will be
left for future work.

The theory presented in the previous sections is explicitly formulated for systems at low density. In this limit, structural correlations are dominated by otherwise isolated pairs of strongly pinned flux lines. Thus, the vectorial nature of their interaction forces need not be considered. At higher densities, each flux line interacts significantly with several neighbors and the vectorial nature of their forces must be taken into account. Constructing a more comprehensive theory valid at higher densities, while beyond the scope of the current paper, is currently under active investigation.

We now turn to a comparison of the qualitative features of the
experimentally obtained pair correlation functions with those obtained
from simulation.
We find that the width and location of the first peak
of *g*(*r*) is
different: while the first peak of the pair correlation function as
obtained from experiments (*cf. *Fig. 1)
is broad and occurs around the mean flux line spacing,
we see a much narrower peak in our simulations
(*cf. *Fig. 2).
Moreover the
first peak occurs at a distance significantly
smaller than the mean flux line
spacing.
Thus the numerical simulations have larger fluctuations in
the local flux line density than are seen in experiment. A reason for this
is that our particle-like treatment of flux lines ignores their magnetic
properties.
One expects that including boundary conditions for
a uniform applied external magnetic field would favor a homogeneous flux line
concentration and thus would penalize the large fluctuations in our
simulations.

We thank Gene Mazenko and Stuart Rice for enlightening discussions. This work was supported in part by the National Science Foundation through the Science and Technology Center for Superconductivity under Award Number DMR-9120000 and in part by the MRSEC program of the National Science Foundation under Award Number DMR-9400379. C. H. S. would like to acknowledge the support of the National University of Singapore. M. M. acknowledges partial support from the Kerpisçi Foundation.