Droplet structure in Ising and Potts models

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Abstract
The structure of a recently introduced droplet in the q-state Potts model is analysed. The authors derive exact relations from which it follows that the incipient infinite droplet at the critical temperature is a self-similar fractal made of links and blobs, just as recently found in random percolation. The number of links Nlinks between two points separated by a distance of the order b is given by Nlinks varies as b1 nu B(q)/ where nu B(q) is the connectedness length exponent when T=Tc(q) and pB is used as an independent variable. This result and the available calculations of nu B(q) indicate that the number of links decreases as q increases. An analysis of the structure of the usual clusters made of nearest-neighbour sites in a given Potts site configuration is also made. In particular, it shows that for d=2 the incipient infinite cluster is made only of blobs and no links.
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