### Abstract

It is proved that every dynamic Monte Carlo algorithm for the self-avoiding walk based on a finite repertoire of local, N-conserving elementary moves is nonergodic (here N is the number of bonds in the walk). Indeed, for large N, each ergodic class forms an exponentially small fraction of the whole space. This invalidates (at least in principle) the use of the Verdier-Stockmayer algorithm and its generalizations for high-precision Monte Carlo studies of the self-avoiding walk.

Original language | English (US) |
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Pages (from-to) | 573-595 |

Number of pages | 23 |

Journal | Journal of Statistical Physics |

Volume | 47 |

Issue number | 3-4 |

DOIs | |

State | Published - May 1987 |

### Fingerprint

### Keywords

- algorithm
- ergodicity
- lattice model
- Monte Carlo
- polymer
- Self-avoiding walk
- Verdier-Stockmayer

### ASJC Scopus subject areas

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

### Cite this

*Journal of Statistical Physics*,

*47*(3-4), 573-595. https://doi.org/10.1007/BF01007527

**Nonergodicity of local, length-conserving Monte Carlo algorithms for the self-avoiding walk.** / Madras, Neal; Sokal, Alan D.

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 47, no. 3-4, pp. 573-595. https://doi.org/10.1007/BF01007527

}

TY - JOUR

T1 - Nonergodicity of local, length-conserving Monte Carlo algorithms for the self-avoiding walk

AU - Madras, Neal

AU - Sokal, Alan D.

PY - 1987/5

Y1 - 1987/5

N2 - It is proved that every dynamic Monte Carlo algorithm for the self-avoiding walk based on a finite repertoire of local, N-conserving elementary moves is nonergodic (here N is the number of bonds in the walk). Indeed, for large N, each ergodic class forms an exponentially small fraction of the whole space. This invalidates (at least in principle) the use of the Verdier-Stockmayer algorithm and its generalizations for high-precision Monte Carlo studies of the self-avoiding walk.

AB - It is proved that every dynamic Monte Carlo algorithm for the self-avoiding walk based on a finite repertoire of local, N-conserving elementary moves is nonergodic (here N is the number of bonds in the walk). Indeed, for large N, each ergodic class forms an exponentially small fraction of the whole space. This invalidates (at least in principle) the use of the Verdier-Stockmayer algorithm and its generalizations for high-precision Monte Carlo studies of the self-avoiding walk.

KW - algorithm

KW - ergodicity

KW - lattice model

KW - Monte Carlo

KW - polymer

KW - Self-avoiding walk

KW - Verdier-Stockmayer

UR - http://www.scopus.com/inward/record.url?scp=34250103739&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34250103739&partnerID=8YFLogxK

U2 - 10.1007/BF01007527

DO - 10.1007/BF01007527

M3 - Article

VL - 47

SP - 573

EP - 595

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 3-4

ER -