Different self-avoiding walks on percolation clusters: A small-cell real-space renormalization-group study

J. P. Hovi; Amnon Aharony

doi:10.1007/BF02183619

Different self-avoiding walks on percolation clusters: A small-cell real-space renormalization-group study

J. P. Hovi, Amnon Aharony

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5 Scopus citations

Abstract

We calculate the average number of steps N for edge-to-edge, "normal," and indefinitely growing self-avoiding walks (SAWs) on two-dimensional critical percolation clusters, using the real-space renormalization-group approach, with small "H" cells. Our results are of the form N = AL^DSAW + B, where L is the end-to-end distance. Similarly to several deterministic fractals, the fractal dimensions D_SAW for these three different kinds of SAWs are found to be equal, and the differences between them appear in the amplitudes A and in the correction terms B. This behavior is attributed to the hierarchical nature of the critical percolation cluster.

Original language	English
Pages (from-to)	1163-1178
Number of pages	16
Journal	Journal of Statistical Physics
Volume	86
Issue number	5-6
DOIs	https://doi.org/10.1007/BF02183619
State	Published - 1 Jan 1997
Externally published	Yes

Keywords

Corrections to scaling
Fractals
Indefinitely growing self-avoiding walks
Percolation clusters
Real-space renormalization group
Self-avoiding walks
Universality

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF02183619

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title = "Different self-avoiding walks on percolation clusters: A small-cell real-space renormalization-group study",

abstract = "We calculate the average number of steps N for edge-to-edge, {"}normal,{"} and indefinitely growing self-avoiding walks (SAWs) on two-dimensional critical percolation clusters, using the real-space renormalization-group approach, with small {"}H{"} cells. Our results are of the form N = ALDSAW + B, where L is the end-to-end distance. Similarly to several deterministic fractals, the fractal dimensions DSAW for these three different kinds of SAWs are found to be equal, and the differences between them appear in the amplitudes A and in the correction terms B. This behavior is attributed to the hierarchical nature of the critical percolation cluster.",

keywords = "Corrections to scaling, Fractals, Indefinitely growing self-avoiding walks, Percolation clusters, Real-space renormalization group, Self-avoiding walks, Universality",

author = "Hovi, {J. P.} and Amnon Aharony",

year = "1997",

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doi = "10.1007/BF02183619",

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volume = "86",

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T1 - Different self-avoiding walks on percolation clusters

T2 - A small-cell real-space renormalization-group study

AU - Hovi, J. P.

AU - Aharony, Amnon

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Y1 - 1997/1/1

N2 - We calculate the average number of steps N for edge-to-edge, "normal," and indefinitely growing self-avoiding walks (SAWs) on two-dimensional critical percolation clusters, using the real-space renormalization-group approach, with small "H" cells. Our results are of the form N = ALDSAW + B, where L is the end-to-end distance. Similarly to several deterministic fractals, the fractal dimensions DSAW for these three different kinds of SAWs are found to be equal, and the differences between them appear in the amplitudes A and in the correction terms B. This behavior is attributed to the hierarchical nature of the critical percolation cluster.

AB - We calculate the average number of steps N for edge-to-edge, "normal," and indefinitely growing self-avoiding walks (SAWs) on two-dimensional critical percolation clusters, using the real-space renormalization-group approach, with small "H" cells. Our results are of the form N = ALDSAW + B, where L is the end-to-end distance. Similarly to several deterministic fractals, the fractal dimensions DSAW for these three different kinds of SAWs are found to be equal, and the differences between them appear in the amplitudes A and in the correction terms B. This behavior is attributed to the hierarchical nature of the critical percolation cluster.

KW - Corrections to scaling

KW - Fractals

KW - Indefinitely growing self-avoiding walks

KW - Percolation clusters

KW - Real-space renormalization group

KW - Self-avoiding walks

KW - Universality

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JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 5-6

ER -

Different self-avoiding walks on percolation clusters: A small-cell real-space renormalization-group study

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Keywords

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