BOUNDARY CONDITION DEPENDENCE OF CLUSTER SIZE RATIOS IN RANDOM PERCOLATION

C. R. da Silva, M. L. Lyra () and G. M. Viswanathan
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C. R. da Silva: Departamento de Física, Universidade Federal de Alagoas, Maceió-AL, 57072-970, Brazil
M. L. Lyra: Departamento de Física, Universidade Federal de Alagoas, Maceió-AL, 57072-970, Brazil
G. M. Viswanathan: Departamento de Física, Universidade Federal de Alagoas, Maceió-AL, 57072-970, Brazil

International Journal of Modern Physics C (IJMPC), 2000, vol. 11, issue 07, 1411-1415

Abstract: We study the ratio of the number of sites in the largest and second largest clusters in random percolation. Using the scaling hypothesis that the ratio / of the mean cluster sizesM1andM2scales asf ((p - pc) L1/ν), we employ finite-size scaling analysis to find that / is nonuniversal with respect to the boundary conditions imposed. The mean of the ratios behaves similarly although with a distinct critical value reflecting the relevance of mass fluctuations at the percolation threshold. These zero exponent ratios also allow for reliable estimates of the critical parameters at percolation from relatively small lattices.

Keywords: Percolation; Cluster Distribution; Critical Ratios (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1142/S0129183100001231

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