Bijection between spin S=pm-1/2 and a cluster of M spins σ=p-1/2

Abstract

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=pM−12 and a cluster of M spins σ=p−12, 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−12 model with general interactions can be reduced to a d-dimensional spin-S model with S=pM−12.