### Abstract

Two directed lattices, the L lattice and Manhattan lattice, are studied. We have calculated exactly the number, the mean-square end-to-end distance, the mean-square radius of gyration and the mean-square distance of a monomer from the origin, for n-step self-avoiding walks on the L lattice and Manhattan lattice for up to 60 and 50 steps, respectively. We have also computed the number and mean-square radius of gyration for self-avoiding polygons on the L lattice and Manhattan lattice for up to 80 and 60 steps, respectively. We have estimated the critical amplitudes and our numerical results are consistent with the conjecture of universality for certain amplitude combinations. However, some amplitude combinations have values different from the corresponding values for undirected lattices.

Original language | English |
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Pages (from-to) | 6927-6938 |

Number of pages | 12 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 32 |

Issue number | 40 |

DOIs | |

Publication status | Published - 1999 Oct 8 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)