Potts q-color field theory and scaling random cluster model |
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Authors: | Gesualdo Delfino Jacopo Viti |
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Institution: | a SISSA, Via Bonomea 265-34136, Trieste, Italy b INFN, Sezione di Trieste, Italy |
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Abstract: | We study structural properties of the q-color Potts field theory which, for real values of q, describes the scaling limit of the random cluster model. We show that the number of independent n-point Potts spin correlators coincides with that of independent n-point cluster connectivities and is given by generalized Bell numbers. Only a subset of these spin correlators enters the determination of the Potts magnetic properties for q integer. The structure of the operator product expansion of the spin fields for generic q is also identified. For the two-dimensional case, we analyze the duality relation between spin and kink field correlators, both for the bulk and boundary cases, obtaining in particular a sum rule for the kink-kink elastic scattering amplitudes. |
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