PERCOLATION PROPERTIES AND UNIVERSALITY CLASS OF A MULTIFRACTAL RANDOM TILING

M. G. Pereira, G. Corso, L. S. Lucena and J. E. Freitas
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M. G. Pereira: International Center for Complex Systems and Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Campus Universitário 59078 970, Natal, RN, Brazil
G. Corso: International Center for Complex Systems and Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Campus Universitário 59078 970, Natal, RN, Brazil;
L. S. Lucena: International Center for Complex Systems and Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Campus Universitário 59078 970, Natal, RN, Brazil
J. E. Freitas: International Center for Complex Systems and Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Campus Universitário 59078 970, Natal, RN, Brazil

International Journal of Modern Physics C (IJMPC), 2005, vol. 16, issue 02, 317-325

Abstract: We study percolation as a critical phenomenon on a random multifractal support. The scaling exponent β related to the mass of the infinite cluster and the fractal dimension of the percolating clusterdfare quantities that have the same value as the ones from the standard two-dimensional regular lattice percolation. The scaling exponent ν related to the correlation length is sensitive to the local anisotropy and assumes a value different from standard percolation. We compare our results with those obtained from the percolation on a deterministic multifractal support. The analysis of ν indicates that the deterministic multifractal is more anisotropic than the random multifractal. We also analyze connections with correlated percolation problems and discuss some possible applications.

Keywords: Percolation; multifractal; correlated percolation; random tiling; petroleum reservoirs; dendrimers (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1142/S0129183105007121

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