Cheon M, Heo M, Chang I, Stauffer D. Fragmentation of percolation clusters in general dimensions.
PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999;
59:R4733-6. [PMID:
11969506 DOI:
10.1103/physreve.59.r4733]
[Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/10/1998] [Indexed: 04/18/2023]
Abstract
The scaling behavior for binary fragmentation of critical percolation clusters in general dimensions is investigated by Monte Carlo simulation as well as by exact series expansions. We obtain values of critical exponents lambda and phi describing the scaling of the fragmentation rate and the distribution of cluster masses produced by binary fragmentation. Our results for lambda and phi in two to nine dimensions agree with the conjectured scaling relation sigma=1+lambda-phi by Edwards and co-workers [Phys. Rev. Lett. 68, 2692 (1992); Phys. Rev. A 46, 6252 (1992)], which in turn excludes the other scaling relations suggested by Gouyet (for d=2), and by Roux and Guyon [J. Phys. A 22, 3693 (1989)], where sigma is the crossover exponent for the cluster numbers in percolation theory.
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