Ij. Tsang et al., Scaling and critical probabilities for cluster size and LA diversity on randomly occupied square lattices, J PHYS A, 33(14), 2000, pp. 2739-2754
Using Monte Carlo simulations, we report the behaviour of the total number
of clusters, the cluster size diversity and the lattice animals (LA) divers
ity on randomly occupied square lattices. The critical probability associat
ed with the maximum of these variables is determined in comparison with the
percolation probability p(c). Our simulations indicate that p(c) and the c
ritical probability of the maximum cluster size diversity p(c) (D-s (max)),
occur at the same point. As indicated in a previous paper (Tsang I R and T
sang I J 1997 J. Phys. A: Math. Gen. 30 L239), the probability for the maxi
mum number of clusters is obtained at a lower value, p(c)(N-max) = 0.27 +/-
0.01. We describe the cluster identification algorithm used to count the d
ifferent LA and determined the critical probability for the maximum LA dive
rsity, p(c)(D-f max) = 0.45 +/- 0.02. We derive the exponents characterizin
g the relation between D-s max, D-f max, and N-max and several scaling rela
tions between the variables measured, the lattice size, and the probability
of occupation p. In addition, we show the scaling behaviour of LA diversit
y versus cluster size diversity for each value of p.