Droplet structure in Ising and Potts models

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 N links between two points separated by a distance of the order b is given by N links varies as b 1 nu B(q)/ where nu B (q) is the connectedness length exponent when T=T c (q) and p B 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.