Bijection between spin and a cluster of spins

We propose a general method by which a spin- S is decomposed into spins less than S . We have obtained the exact mapping between spin S = p M − 1 2 and a cluster of M spins σ = p − 1 2 , where p and M are positive integers. We have discussed the possible applications of such transformations. In particular we have shown how a general d + 1 dimensional spin- p − 1 2 model with general interactions can be reduced to a d -dimensional spin- S model with S = p M − 1 2 .