### 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) |
---|---|

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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

*Journal of Statistical Physics*,

*67*(1-2), 65-111. https://doi.org/10.1007/BF01049027

**Join- and-cut algorithm for self-avoiding walks with variable length and free endpoints.** / Caracciolo, Sergio; Pelissetto, Andrea; Sokal, AJan D.

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 67, no. 1-2, pp. 65-111. https://doi.org/10.1007/BF01049027

}

TY - JOUR

T1 - Join- and-cut algorithm for self-avoiding walks with variable length and free endpoints

AU - Caracciolo, Sergio

AU - Pelissetto, Andrea

AU - Sokal, AJan D.

PY - 1992/4

Y1 - 1992/4

N2 - 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 Ntot 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.

AB - 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 Ntot 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.

KW - critical exponent

KW - join- and-cut algorithm

KW - Monte Carlo

KW - pivot algorithm

KW - polymer

KW - Self-avoiding walk

UR - http://www.scopus.com/inward/record.url?scp=0002685154&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0002685154&partnerID=8YFLogxK

U2 - 10.1007/BF01049027

DO - 10.1007/BF01049027

M3 - Article

VL - 67

SP - 65

EP - 111

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 1-2

ER -