A proper treatment of the droplet model of phase transitions needs some knowledge of the degree of compactness of random clusters. It is pointed out that some numerical evidence on this is already available for both site and bond clusters on the plane square lattice. The domains occurring in a Monte Carlo solution of the percolation problem are found to be highly ramified, those for the Ising and Potts problems less so.
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H. N. V. Temperley (1976) studied this question.
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