Self-avoiding walks on the lattice ${\Bbb Z}^2$ with the 8-neighbourhood system

Volume 28 / 2001

Andrzej Chydzi/nski, Bogdan Smo/lka Applicationes Mathematicae 28 (2001), 169-180 MSC: 82B41, 05A15, 68U10. DOI: 10.4064/am28-2-4

Abstract

This paper deals with the properties of self-avoiding walks defined on the lattice with the 8-neighbourhood system. We compute the number of walks, bridges and mean-square displacement for $N=1$ through 13 ($N$ is the number of steps of the self-avoiding walk). We also estimate the connective constant and critical exponents, and study finite memory and generating functions. We show applications of this kind of walk. In addition, we compute upper bounds for the number of walks and the connective constant.

Authors

  • Andrzej Chydzi/nskiDepartment of Mathematics
    Silesian Technical University
    Kaszubska 23
    44-101 Gliwice, Poland
    e-mail
  • Bogdan Smo/lkaDepartment of Computer Science
    Silesian Technical University
    Akademicka 16
    44-101 Gliwice, Poland
    e-mail

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