The augmented space formalism has been used so far for the study of disordered crystals. We stress here that the topological structure of the augmented space of a binary alloy is formally equivalent to the set of configurations of an Ising system. In particular in both cases a very useful binary representation for labelling the vectors of the space can be done. Starting from this observation we have developed a very efficient description of the Ising hamiltonian, and we have shown that it can be succesfully applied both in the direct diagonalization approach and in conjunction with the renormalization scheme. Within this last case we have proposed a generalization of the techniques commonly used in the literature, obtaining very good results.
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