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Different types of self-avoiding walks on deterministic fractals

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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 then th fractal generation, of linear sizeL, 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 dimensionD saw. However, they have different amplitudes (A) and correction terms (B).

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Authors and Affiliations

  1. School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Ramat Aviv, Israel

    Y. Shussman & A. Aharony

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  1. Y. Shussman
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  2. A. Aharony
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Shussman, Y., Aharony, A. Different types of self-avoiding walks on deterministic fractals. J Stat Phys 77, 545–563 (1994). https://doi.org/10.1007/BF02179449

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  • DOI: https://doi.org/10.1007/BF02179449

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