  We use a random pinning procedure to study amorphous order in two glassy spin
models. On increasing the concentration of pinned spins at constant
temperature, we find a sharp crossover (but no thermodynamic phase transition)
from bulk relaxation to localisation in a single state. At low temperatures,
both models exhibit scaling behaviour. We discuss the growing length and time
scales associated with amorphous order, and the fraction of pinned spins
required to localize the system in a single state. These results, obtained for
finite dimensional interacting models, provide a theoretical scenario for the
effect of random pinning that differs qualitatively from previous approaches
based either on mean-field, mode-coupling, or renormalization group reatments.
