### 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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

*Journal of Statistical Physics*,

*120*(5-6), 1037-1100. https://doi.org/10.1007/s10955-005-7004-3

**Correction-to-scaling exponents for two-dimensional self-avoiding walks.** / Caracciolo, Sergio; Guttmann, Anthony J.; Jensen, Iwan; Pelissetto, Andrea; Rogers, Andrew N.; Sokal, Alan D.

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 120, no. 5-6, pp. 1037-1100. https://doi.org/10.1007/s10955-005-7004-3

}

TY - JOUR

T1 - Correction-to-scaling exponents for two-dimensional self-avoiding walks

AU - Caracciolo, Sergio

AU - Guttmann, Anthony J.

AU - Jensen, Iwan

AU - Pelissetto, Andrea

AU - Rogers, Andrew N.

AU - Sokal, Alan D.

PY - 2005/9

Y1 - 2005/9

N2 - 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 Δ1=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.

AB - 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 Δ1=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.

KW - Conformal invariance

KW - Corrections to scaling

KW - Critical exponents

KW - Exact enumeration

KW - Monte Carlo

KW - Pivot algorithm

KW - Polymer

KW - Self-avoiding walk

KW - Series expansion

UR - http://www.scopus.com/inward/record.url?scp=27844546229&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=27844546229&partnerID=8YFLogxK

U2 - 10.1007/s10955-005-7004-3

DO - 10.1007/s10955-005-7004-3

M3 - Article

AN - SCOPUS:27844546229

VL - 120

SP - 1037

EP - 1100

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 5-6

ER -