  We show that elastic interactions of an array of self-assembled quantum dots
in a parent material matrix are markedly distinct from the elastic field
created by a single point defect, and can explain the observed abrupt
correlation--anticorrelation transition in semiconductor quantum dot stacks.
Finite volume effects of the quantum dots are shown to lead to sharper
transitions. Our analysis also predicts the inclination angle under which the
alignment in successive quantum dot layers occurs in dependence on the material
anisotropy.
