  We analyze the induced interactions between localized holes in weakly-doped
Heisenberg antiferromagnets due to the modification of the quantum zero point
spin wave energy; i.e. the analogue of the Casimir effect. We show that this
interaction is uniformly attractive and falls off as r^{-2 d+1} in d
dimensions. For ``stripes'', i.e parallel (d-1)-dimensional hypersurfaces of
localized holes, the interaction energy per unit hyperarea is attractive and
falls, generically, like r^{-d}. We argue that, in the absence of a long-range
Coulomb repulsion between holes, this interaction leads to an instability of
any charge-ordered state in the dilute doping limit.
