### Abstract

We introduce a new Monte Carlo algorithm for the self-avoiding walk (SAW), and show that it is particularly efficient in the critical region (long chains). We also introduce new and more efficient statistical techniques. We employ these methods to extract numerical estimates for the critical parameters of the SAW on the square lattice. We find μ=2.63820 ± 0.00004 ± 0.00030 γ=1.352 ± 0.006 ± 0.025 νv=0.7590 ± 0.0062 ± 0.0042 where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second bar represents statistical error (classical 95% confidence limits). These results are based on SAWs of average length ≈ 166, using 340 hours CPU time on a CDC Cyber 170-730. We compare our results to previous work and indicate some directions for future research.

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

Pages (from-to) | 483-531 |

Number of pages | 49 |

Journal | Journal of Statistical Physics |

Volume | 40 |

Issue number | 3-4 |

DOIs | |

State | Published - Aug 1985 |

### Fingerprint

### Keywords

- algorithm
- critical exponents
- lattice model
- maximum-likelihood estimation
- Monte Carlo
- polymer
- Self-avoiding walk

### ASJC Scopus subject areas

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

### Cite this

*Journal of Statistical Physics*,

*40*(3-4), 483-531. https://doi.org/10.1007/BF01017183

**New Monte Carlo method for the self-avoiding walk.** / Berretti, Alberto; Sokal, Alan D.

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 40, no. 3-4, pp. 483-531. https://doi.org/10.1007/BF01017183

}

TY - JOUR

T1 - New Monte Carlo method for the self-avoiding walk

AU - Berretti, Alberto

AU - Sokal, Alan D.

PY - 1985/8

Y1 - 1985/8

N2 - We introduce a new Monte Carlo algorithm for the self-avoiding walk (SAW), and show that it is particularly efficient in the critical region (long chains). We also introduce new and more efficient statistical techniques. We employ these methods to extract numerical estimates for the critical parameters of the SAW on the square lattice. We find μ=2.63820 ± 0.00004 ± 0.00030 γ=1.352 ± 0.006 ± 0.025 νv=0.7590 ± 0.0062 ± 0.0042 where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second bar represents statistical error (classical 95% confidence limits). These results are based on SAWs of average length ≈ 166, using 340 hours CPU time on a CDC Cyber 170-730. We compare our results to previous work and indicate some directions for future research.

AB - We introduce a new Monte Carlo algorithm for the self-avoiding walk (SAW), and show that it is particularly efficient in the critical region (long chains). We also introduce new and more efficient statistical techniques. We employ these methods to extract numerical estimates for the critical parameters of the SAW on the square lattice. We find μ=2.63820 ± 0.00004 ± 0.00030 γ=1.352 ± 0.006 ± 0.025 νv=0.7590 ± 0.0062 ± 0.0042 where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second bar represents statistical error (classical 95% confidence limits). These results are based on SAWs of average length ≈ 166, using 340 hours CPU time on a CDC Cyber 170-730. We compare our results to previous work and indicate some directions for future research.

KW - algorithm

KW - critical exponents

KW - lattice model

KW - maximum-likelihood estimation

KW - Monte Carlo

KW - polymer

KW - Self-avoiding walk

UR - http://www.scopus.com/inward/record.url?scp=34250112054&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34250112054&partnerID=8YFLogxK

U2 - 10.1007/BF01017183

DO - 10.1007/BF01017183

M3 - Article

VL - 40

SP - 483

EP - 531

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 3-4

ER -