  We study the effects of magneto-elastic coupling on the degenerate ground
state of the antiferromagnetic Heisenberg model on regular triangle and
tetrahedron clusters of spin-1/2. Both give very similar results. Static
distortion lifts the degeneracy of the ground state through the distance
dependence of the exchange coupling. On the contrary, quantum-mechanical or
dynamical distortion does not. The tetragonal distortion at the non-magnetic
phase transition of spinels is discussed.
