## Abstract

We study the correction-to-scaling exponents for the two-dimensional self-avoiding walk, using a combination of series-extrapolation and Monte Carlo methods. We enumerate all self-avoiding walks up to 59 steps on the square lattice, and up to 40 steps on the triangular lattice, measuring the mean-square end-to-end distance, the mean-square radius of gyration and the mean-square distance of a monomer from the endpoints. The complete endpoint distribution is also calculated for self-avoiding walks up to 32 steps (square) and up to 22 steps (triangular). We also generate self-avoiding walks on the square lattice by Monte Carlo, using the pivot algorithm, obtaining the mean-square radii to ≈ 0.01% accuracy up to N=4000. We give compelling evidence that the first non-analytic correction term for two-dimensional self-avoiding walks is Δ_{1}=3/2. We compute several moments of the endpoint distribution function, finding good agreement with the field-theoretic predictions. Finally, we study a particular invariant ratio that can be shown, by conformal-field-theory arguments, to vanish asymptotically, and we find the cancellation of the leading analytic correction.

Original language | English (US) |
---|---|

Pages (from-to) | 1037-1100 |

Number of pages | 64 |

Journal | Journal of Statistical Physics |

Volume | 120 |

Issue number | 5-6 |

DOIs | |

State | Published - Sep 2005 |

## Keywords

- Conformal invariance
- Corrections to scaling
- Critical exponents
- Exact enumeration
- Monte Carlo
- Pivot algorithm
- Polymer
- Self-avoiding walk
- Series expansion

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics