  We show that the process of spontaneous symmetry breaking can trap a field
theoretic system in a highly non-trivial state containing a lattice of domain
walls. In one large compact space dimension, a lattice is inevitably formed. In
two dimensions, the probability of lattice formation depends on the ratio of
sizes L_x, L_y of the spatial dimensions. We find that a lattice can form even
if R=L_y/L_x is of order unity. We numerically determine the number of walls in
the lattice as a function of L_x and L_y.
