Universal mass ratios of non-unique spanning clusters in percolation

Parongama Sen; Amnon Aharony

doi:10.1142/S012918319700103X

Universal mass ratios of non-unique spanning clusters in percolation

Parongama Sen, Amnon Aharony

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We find that when two or more spanning clusters exist at the percolation threshold, the mass of each scales with the same fractal dimension D = 1.89 in two dimensions and D = 2.53 in three dimensions. We also determine the ratios of the masses of the spanning clusters. In two dimensions, this is done for different lattices of different shapes. In the case of two spanning clusters, the ratio of the larger spanning cluster to the smaller lies around 1.4 for two dimensions, almost independent of lattice structure and shape.

Original language	English
Pages (from-to)	1169-1173
Number of pages	5
Journal	International Journal of Modern Physics C
Volume	8
Issue number	5
DOIs	https://doi.org/10.1142/S012918319700103X
State	Published - 1 Jan 1997
Externally published	Yes

Keywords

Fractal Dimension
Spanning Probabilities

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy
Computer Science Applications
Computational Theory and Mathematics

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10.1142/S012918319700103X

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abstract = "We find that when two or more spanning clusters exist at the percolation threshold, the mass of each scales with the same fractal dimension D = 1.89 in two dimensions and D = 2.53 in three dimensions. We also determine the ratios of the masses of the spanning clusters. In two dimensions, this is done for different lattices of different shapes. In the case of two spanning clusters, the ratio of the larger spanning cluster to the smaller lies around 1.4 for two dimensions, almost independent of lattice structure and shape.",

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AU - Aharony, Amnon

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AB - We find that when two or more spanning clusters exist at the percolation threshold, the mass of each scales with the same fractal dimension D = 1.89 in two dimensions and D = 2.53 in three dimensions. We also determine the ratios of the masses of the spanning clusters. In two dimensions, this is done for different lattices of different shapes. In the case of two spanning clusters, the ratio of the larger spanning cluster to the smaller lies around 1.4 for two dimensions, almost independent of lattice structure and shape.

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KW - Spanning Probabilities

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Universal mass ratios of non-unique spanning clusters in percolation

Abstract

Keywords

ASJC Scopus subject areas

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