Abstract
We use a cluster-decomposition technique to derive a functional integral representation of the partition function of quantum spin systems on a lattice. The free energy is decomposed into the sum of the free energy of the isolated clusters and that of a system of interacting vector fields. Our formalism allows a constraint-free description of the thermodynamics and excitations in the rotationally invariant phase. The transition to the broken-symmetry phases appears to be linked to the softening of spin wave modes. We briefly discuss applications to one- and two- dimensional spin systems.
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