Different types of self-avoiding walks on deterministic fractals

Y. Shussman; A. Aharony

doi:10.1007/BF02179449

Different types of self-avoiding walks on deterministic fractals

Y. Shussman, A. Aharony

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

1 Scopus citations

Abstract

"Normal" and indefinitely-growing (IG) self-avoiding walks (SAWs) are exactly enumerated on several deterministic fractals (the Manderbrot-Given curve with and without dangling bonds, and the 3-simplex). On the n th fractal generation, of linear size L, the average number of steps behaves asymptotically as 〈N〉=AL^D_saw+B. In contrast to SAWs on regular lattices, on these factals IGSAWs and "normal" SAWs have the same fractal dimension D_saw. However, they have different amplitudes (A) and correction terms (B).

Original language	English
Pages (from-to)	545-563
Number of pages	19
Journal	Journal of Statistical Physics
Volume	77
Issue number	3-4
DOIs	https://doi.org/10.1007/BF02179449
State	Published - 1 Nov 1994
Externally published	Yes

Keywords

Self-avoiding walks
fractals
indefinitely-growing self-avoiding walks
renormalization

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF02179449

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AB - "Normal" and indefinitely-growing (IG) self-avoiding walks (SAWs) are exactly enumerated on several deterministic fractals (the Manderbrot-Given curve with and without dangling bonds, and the 3-simplex). On the n th fractal generation, of linear size L, the average number of steps behaves asymptotically as 〈N〉=ALDsaw+B. In contrast to SAWs on regular lattices, on these factals IGSAWs and "normal" SAWs have the same fractal dimension Dsaw. However, they have different amplitudes (A) and correction terms (B).

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KW - renormalization

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ER -

Different types of self-avoiding walks on deterministic fractals

Abstract

Keywords

ASJC Scopus subject areas

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