Cluster diversity and entropy on the percolation model : the lattice animal identification algorithm
Cluster diversity and entropy on the percolation model : the lattice animal identification algorithm
Faculty of Sciences. Physics

article

2000
Lancaster, Pa
, 2000

Physics

Physical review : E : statistical physics, plasmas, fluids, and related interdisciplinary topics. - Lancaster, Pa, 1993 - 2000

62(2000)
:5 Part a
, p. 6004-6014

1063-651X

000165341700025

E

English (eng)

University of Antwerp

We present an algorithm to identify and count different lattice animals (LA's) in the site-percolation model. This algorithm allows a definition of clusters based on the distinction of cluster shapes, in contrast with the well-known Hoshen-Kopelman algorithm, in which the clusters are differentiated by their sizes. It consists in coding each unit. cell of a cluster according to the nearest neighbors (NN) and ordering the codes in a proper sequence. In this manner, a LA is represented by a specific code sequence. In addition, with some modification the algorithm is capable of differentiating between fixed and free LA's. The enhanced Hoshen-Kopelman algorithm [J. Hoshen, 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 simulations on planar square lattices up to 2000x2000, we apply this algorithm to the percolation model. We calculate the cluster diversity and cluster entropy of the system, which leads to the determination of probabilities associated with the maximum of these functions. We show that these critical probabilities are associated with the percolation transition and with the complexity of the system.

https://repository.uantwerpen.be/docman/irua/2db18b/6087.pdf

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