Density profile of the incipient infinite percolation cluster

Dietrich Stauffer; Amnon Aharony

doi:10.1142/S0129183199000735

Density profile of the incipient infinite percolation cluster

Dietrich Stauffer, Amnon Aharony

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

7 Scopus citations

Abstract

Monte Carlo simulations show simple scaling for the number of sites in the spanning cluster at the percolation threshold as a function of distance from the border. The results for free boundary conditions represent crossover from surface to bulk fractal dimensions, and the former agrees with exact results in d = 2 and d = 6 - ∈ dimensions and with earlier simulations. We also present and explain results for bus-bar boundary conditions, with two types of connection rules. The scaling functions, which are predicted to be universal, surprisingly seem not to depend on the aspect ratios of the samples.

Original language	English
Pages (from-to)	935-940
Number of pages	6
Journal	International Journal of Modern Physics C
Volume	10
Issue number	5
DOIs	https://doi.org/10.1142/S0129183199000735
State	Published - 1 Jan 1999
Externally published	Yes

Keywords

Connectivity Function
Critical Exponents
Dimensionality Dependence

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/S0129183199000735

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abstract = "Monte Carlo simulations show simple scaling for the number of sites in the spanning cluster at the percolation threshold as a function of distance from the border. The results for free boundary conditions represent crossover from surface to bulk fractal dimensions, and the former agrees with exact results in d = 2 and d = 6 - ∈ dimensions and with earlier simulations. We also present and explain results for bus-bar boundary conditions, with two types of connection rules. The scaling functions, which are predicted to be universal, surprisingly seem not to depend on the aspect ratios of the samples.",

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AU - Aharony, Amnon

PY - 1999/1/1

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N2 - Monte Carlo simulations show simple scaling for the number of sites in the spanning cluster at the percolation threshold as a function of distance from the border. The results for free boundary conditions represent crossover from surface to bulk fractal dimensions, and the former agrees with exact results in d = 2 and d = 6 - ∈ dimensions and with earlier simulations. We also present and explain results for bus-bar boundary conditions, with two types of connection rules. The scaling functions, which are predicted to be universal, surprisingly seem not to depend on the aspect ratios of the samples.

AB - Monte Carlo simulations show simple scaling for the number of sites in the spanning cluster at the percolation threshold as a function of distance from the border. The results for free boundary conditions represent crossover from surface to bulk fractal dimensions, and the former agrees with exact results in d = 2 and d = 6 - ∈ dimensions and with earlier simulations. We also present and explain results for bus-bar boundary conditions, with two types of connection rules. The scaling functions, which are predicted to be universal, surprisingly seem not to depend on the aspect ratios of the samples.

KW - Connectivity Function

KW - Critical Exponents

KW - Dimensionality Dependence

UR - https://www.scopus.com/pages/publications/0033476759

U2 - 10.1142/S0129183199000735

DO - 10.1142/S0129183199000735

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JO - International Journal of Modern Physics C

JF - International Journal of Modern Physics C

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ER -

Density profile of the incipient infinite percolation cluster

Abstract

Keywords

ASJC Scopus subject areas

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