  Snapshots of colloidal particles moving on disordered two-dimensional
substrates can be used to extract equal-time many-body correlations in their
positions. To understand the systematics of these correlations, we perform
Monte Carlo simulations of a two-dimensional model fluid placed in a quenched
disordered background. We use configurations generated from these simulations
to compute translational and orientational two-point correlations at equal
time, concentrating on correlations in local orientational order as a function
of density and disorder strength. We calculate both the disorder averaged
version of conventional two-point correlation functions for orientational
order, as well as the disorder averaged version of a novel correlation function
of time-averaged disorder-induced inhomogeneities in local orientation
analogous to the Edwards-Anderson correlation function in spin systems. We
demonstrate that these correlations can exhibit interesting non-monotonic
behavior in proximity to the underlying fluid-solid transition and suggest that
this prediction should be experimentally accessible.
