Clusters and droplets in the q-state Potts model

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Abstract
A Potts correlated polychromatic percolation is studied. The clusters are made of sites corresponding to a given value of the q-state Potts variables, connected by bonds being active with probability pB. To treat this problem an s-state Potts Hamiltonian diluted with q-state Potts variables (instead of lattice gas variables) is introduced to which the the Migdal-Kadanoff renormalisation group is applied. It is found for a particular choice of pB=1-e-K (where K is the Potts coupling constant divided by the Boltzmann factor) that these clusters, called droplets diverge at the Potts critical point with Potts exponents.