  The density and correlations of topological defects are investigated
numerically in a model of a d=2 elastic medium subject to a periodic quenched
random potential. The computed density of defects decreases approximately
exponentially with the defect core energy. Comparing the defect-free ground
state with the ground state with defects, it is found that the difference is
described by string-like excitations, bounded by defect pairs, which have a
fractal dimension of 1.250(3). At zero temperature, the disorder-induced
defects screen the interaction of introduced vortex pairs.
