Abstract
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 because of the characteristics of their symmetry. Quantum-mechanical distortion appears through fluctuation of normal modes and the degeneracy of the ground state is not lifted. The tetragonal distortion at the non-magnetic phase transition of vanadium spinels is discussed.
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