Title
Scaling and critical probabilities for cluster size and LA diversity on randomly occupied square latticesScaling and critical probabilities for cluster size and LA diversity on randomly occupied square lattices
Author
Faculty/Department
Faculty of Sciences. Physics
Research group
Vision lab
Publication type
article
Publication
London,
Subject
Physics
Source (journal)
Journal of physics: A: mathematical and general. - London, 1968 - 2006
Volume/pages
33(2000):14, p. 2739-2754
ISSN
0305-4470
ISI
000087825600011
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
Using Monte Carlo simulations, we report the behaviour of the total number of clusters, the cluster size diversity and the lattice animals (LA) diversity on randomly occupied square lattices. The critical probability associated with the maximum of these variables is determined in comparison with the percolation probability p(c). Our simulations indicate that p(c) and the critical 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 Tsang I J 1997 J. Phys. A: Math. Gen. 30 L239), the probability for the maximum 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 different LA and determined the critical probability for the maximum LA diversity, p(c)(D-f max) = 0.45 +/- 0.02. We derive the exponents characterizing the relation between D-s max, D-f max, and N-max and several scaling relations between the variables measured, the lattice size, and the probability of occupation p. In addition, we show the scaling behaviour of LA diversity versus cluster size diversity for each value of p.
Full text (open access)
https://repository.uantwerpen.be/docman/irua/515474/6096.pdf
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