We consider a two-dimensional system of *N* particles
in a quenched random
pinscape consisting of discrete pinning sites positioned at random.
The particles, which can be interpreted as
stiff magnetic flux lines, have positions that are
specified by (two-dimensional) vectors .
As a convention, particle and pinning site locations
are subscripted with Latin and Greek indices, respectively.
The force on the *i*^{th} flux line at position
is given by

Here the first and second sum are the contributions to the total force on a given particle due to its interactions with the other particles and with the pinning sites;

where is the pin's strength, and

The locations of the pinning sites
are assumed to be distributed
at random. We seek stable and static flux line configurations
given by solutions to

with the additional stability constraint that the matrix be positive-definite. If is such a configuration, the pair correlation function

with

(7) |

and denoting an average over angles. The pair correlation function

If the analogy to liquid structure theory adequately describes the
emergence of structure in this quenched random system, then
Eqs. (1) and (2) imply that (to lowest order)

Thus liquid theory predicts that a plot of the corresponding quantity versus

Our numerical work involves solving Eq. (5) for static configurations and thereby obtaining the configuration-averaged pair correlation function. Details of the implementation and presentation of our numerical results are given in the following two sections.