Shape and size of two-dimensional percolation clusters with and without correlations

Abstract

The statistical analysis previously used for the temperature behaviour of clusters for the Ising model is applied to Monte Carlo samples of percolation clusters. Three cases are considered: (a) positive correlation (T=2T_c ferromagnetic): (b) random (T= infinity ); (c) negative correlation (T=2T_c antiferromagnetic). It is found that the exponents which characterise the decay of the cluster-size distributions do not depend on correlation. These distributions can be fitted over their whole range by assuming that percolation critical exponents are independent of correlation, but the scaling functions which then result do depend on correlation. Statistical parameters which are related to the compactness or ramification of clusters change smoothly with correlation. However, some features of negative correlation are significantly different in behaviour.