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Critical behavior of self-avoiding walks on fractals

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Abstract

Using a new graph counting technique suitable for self-similar fractals, exact 18th-order series expansions for SAWs on some Sierpinski carpets are generated. From them, the critical fugacityx c and critical exponents ΝSAW and γSAW are obtained. The results show a linear dependence of the critical fugacity with the average number of bonds per site of the lattices studied. We find for some carpets with low lacunarity that ΝSAW<0.75, thus violating the relation ΝSAW(fractal) > ΝSAW (d) for SAWs on the fractals which are embedded in ad-dimensional Euclidean space.

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Authors and Affiliations

  1. Departamento de Física, Pontificia Universidade Católica do Rio de Janeiro, 22452, Rio de Janeiro RJ, Brazil

    Fábio D. A. Aarão Reis & R. Riera

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  1. Fábio D. A. Aarão Reis
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  2. R. Riera
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Reis, F.D.A.A., Riera, R. Critical behavior of self-avoiding walks on fractals. J Stat Phys 71, 453–470 (1993). https://doi.org/10.1007/BF01058432

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  • DOI: https://doi.org/10.1007/BF01058432

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