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The critical behaviour of two-dimensional self-avoiding random walks

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Zeitschrift für Physik B Condensed Matter

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Abstract

We present exact results for the mean end-to-end distance of self-avoiding random walks on several planar lattices. For the square lattice, we extend the known results from walks with ≦20 steps to walks with ≦22 steps, and for the triagular lattice from 14 to 16 steps. For the honeycomb lattice we went up to 34 steps, for the two-choice square lattice up to 44 steps, and for the 4-choice triagular lattice up to 19 steps. The extrapolated valuev=0.747±0.001 (provided the correction-to-scalng exponent is not appreaciably smaller than unity) is in disagreement with both Flory's value and the recent estimate of Derrida. We claim that a different analysis of Derrida's data supports this value.

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Authors and Affiliations

  1. Fachbereich 8-Physik, Universität Wuppertal, Germany

    P. Grassberger

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  1. P. Grassberger
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Address from 1st April–30th September 1982: Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel

Address from 1st April-30th September 1982, Department of Chemical Physics, Weizmann Institute of Science, Rehovot, 76100, Israel

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Grassberger, P. The critical behaviour of two-dimensional self-avoiding random walks. Z. Physik B - Condensed Matter 48, 255–260 (1982). https://doi.org/10.1007/BF01420588

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  • DOI: https://doi.org/10.1007/BF01420588

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