Potts q-color field theory and scaling random cluster model
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.
Keywords
Cite
@article{arxiv.1104.4323,
title = {Potts q-color field theory and scaling random cluster model},
author = {Gesualdo Delfino and Jacopo Viti},
journal= {arXiv preprint arXiv:1104.4323},
year = {2015}
}
Comments
27 pages; 6 figures. Published version, some comments and references added