  As a simplified model of randomly pinned vortex lattices or charge-density
waves, we study the random-field XY model on square ($d=2$) and simple cubic
($d=3$) lattices. We argue, and confirm in simulations, that the spacing
between topological defects (vortices) diverges more strongly than the Imry-Ma
pinning length as the random field strength, $H$, is reduced. For $d=3$ the
data are consistent with a topological phase transition at a nonzero $H_c$ to a
vortex-free pinned phase.

Condensed Matter