We consider theories with late-time phase transitions that lead to the
formation of energetically soft domain wall defects. These transition
s occur in the vacuum state of a weakly coupled scalar field which is
not in thermal equilibrium. The spatial properties and distribution of
these domain walls are computed using percolation theory. Assuming sp
herical collapse of matter, the percolation results are used to accura
tely predict the richness distribution of Abell clusters.