Cluster diversity and entropy on the percolation model: The lattice animalidentification algorithm

We present an algorithm to identify and count different lattice animals (LA 's) in the site-percolation model. This algorithm allows a definition of cl usters based on the distinction of cluster shapes, in contrast with the wel l-known Hoshen-Kopelman algorithm, in which the clusters are differentiated by their sizes. It consists in coding each unit. cell of a cluster accordi ng to the nearest neighbors (NN) and ordering the codes in a proper sequenc e. In this manner, a LA is represented by a specific code sequence. In addi tion, with some modification the algorithm is capable of differentiating be tween fixed and free LA's. The enhanced Hoshen-Kopelman algorithm [J. Hoshe n, M. W. Berry, and K. S. Minser, Phys. Rev. E 56, 1455 (1997)] is used to compose the set of NN code sequences of each cluster. Using Monte Carlo sim ulations on planar square lattices up to 2000x2000, we apply this algorithm to the percolation model. We calculate the cluster diversity and cluster e ntropy of the system, which leads to the determination of probabilities ass ociated with the maximum of these functions. We show that these critical pr obabilities are associated with the percolation transition and with the com plexity of the system.