  XY and Heisenberg spins, subjected to strong random fields acting at few
points in space with concentration $c_r \ll 1$, are studied numerically on 3d
lattices containing over four million sites. Glassy behavior with strong
dependence on initial conditions is found. Beginning with a random initial
orientation of spins, the system evolves into ferromagnetic domains inversely
proportional to $c_r$ in size. The area of the hysteresis loop, $m(H)$, scales
as $c_r^2$. These findings are explained by mapping the effect of strong dilute
random field onto the effect of weak continuous random field. Our theory
applies directly to ferromagnets with magnetic impurities, and is conceptually
relevant to strongly pinned vortex lattices in superconductors and pinned
charge density waves.
