Cluster shapes in lattice gases and percolation

An analysis is undertaken of the mean surface s of clusters of size n from Monte Carlo data simulating a two-dimensional Ising model. At sufficiently high temperatures the data represent a percolation process and it is found that the clusters are completely ramified (tree- or sponge-like). At temperatures just below T_c the data do not correspond to circular droplets as assumed in standard nucleation theory and typical samples show a great deal of ramification. It is concluded that the parameters in Fisher's droplet model are empirical and should not be given a direct physical interpretation.