Potts q-color field theory and scaling random cluster model

Details Potts q-color field theory and scaling random cluster model Potts q-color field theory and scaling random cluster model

2011-04-21

arxiv.org/abs/1104.4323v2

Nucl.Phys.B852:149-173,2011

Physics

High Energy Physics

High Energy Physics - Theory

27 pages; 6 figures. Published version, some comments and references added

Scientific paper

10.1016/j.nuclphysb.2011.06.012

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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