### Green Functions for Spin Clusters via Computer Algebra

#### Resumo

Green Functions for spin clusters (from two to five spins, with quantum numbers S =1/2 and S = 1) were analytically derived and excitation energies (the poles of the Green Functions) directly revealed. An extended representation of the spin operators made it possible to deal with the Green functions equations of motion algebraically, allowing the use of simple computer algebra techniques to deduce the exact Green Functions; computer algebra also proved to be effective in obtaining energy levels. The values of the energies of the levels and the transition energies increase with the size of the cluster; clusters of equal number of spins but with different geometries have the same transition energies, however, the more symmetrical ones have energy degeneracies.

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