## Abstract

We introduce a new Monte Carlo algorithm for generating self-avoiding walks of variable length and free endpoints. The algorithm works in the unorthodox ensemble consisting of all pairs of SAWs such that the total number of steps N_{tot} in the two walks is fixed. The elementary moves of the algorithm are fixed-N (e.g., pivot) moves on the individual walks, and a novel "join- and-cut" move that concatenates the two walks and then cuts them at a random location. We analyze the dynamic critical behavior of the new algorithm, using a combination of rigorous, heuristic, and numerical methods. In two dimensions the autocorrelation time in CPU units grows as N^{≈1.5}, and the behavior improves in higher dimensions. This algorithm allows high-precision estimation of the critical exponent γ.

Original language | English (US) |
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Pages (from-to) | 65-111 |

Number of pages | 47 |

Journal | Journal of Statistical Physics |

Volume | 67 |

Issue number | 1-2 |

DOIs | |

State | Published - Apr 1992 |

## Keywords

- Monte Carlo
- Self-avoiding walk
- critical exponent
- join- and-cut algorithm
- pivot algorithm
- polymer

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics