### Abstract

A massively parallel supercamputer was nsed to exhaustively enumerate all of the Hamiltonian walks for simple cubic sublattices of four different sizes (up to 3 × 4 × 4). The behaviour of the logarithm of the number of walks was found to be linear in the number of vertices in the lattice. The linear fit is shown to agree also with the asymptotic limit of the Flory mean field theoretical estimate Thus, we suggest that the fit obtained yields the number of walks for any size fragment of the cubic Imice to logarithmic accuracy. The significance of this result to the validily of polymer models is also discussed.

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

Pages (from-to) | 6231-6236 |

Number of pages | 6 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 27 |

Issue number | 18 |

DOIs | |

State | Published - Sep 21 1994 |

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### ASJC Scopus subject areas

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

### Cite this

*Journal of Physics A: Mathematical and General*,

*27*(18), 6231-6236. https://doi.org/10.1088/0305-4470/27/18/030

**Enumerations of the Hamiltonian walks on a cubic sublattice.** / Pande, Vijay S.; Joerg, Chris; Yu Grosberg, Alexander; Tanka, Toyoichi.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 27, no. 18, pp. 6231-6236. https://doi.org/10.1088/0305-4470/27/18/030

}

TY - JOUR

T1 - Enumerations of the Hamiltonian walks on a cubic sublattice

AU - Pande, Vijay S.

AU - Joerg, Chris

AU - Yu Grosberg, Alexander

AU - Tanka, Toyoichi

PY - 1994/9/21

Y1 - 1994/9/21

N2 - A massively parallel supercamputer was nsed to exhaustively enumerate all of the Hamiltonian walks for simple cubic sublattices of four different sizes (up to 3 × 4 × 4). The behaviour of the logarithm of the number of walks was found to be linear in the number of vertices in the lattice. The linear fit is shown to agree also with the asymptotic limit of the Flory mean field theoretical estimate Thus, we suggest that the fit obtained yields the number of walks for any size fragment of the cubic Imice to logarithmic accuracy. The significance of this result to the validily of polymer models is also discussed.

AB - A massively parallel supercamputer was nsed to exhaustively enumerate all of the Hamiltonian walks for simple cubic sublattices of four different sizes (up to 3 × 4 × 4). The behaviour of the logarithm of the number of walks was found to be linear in the number of vertices in the lattice. The linear fit is shown to agree also with the asymptotic limit of the Flory mean field theoretical estimate Thus, we suggest that the fit obtained yields the number of walks for any size fragment of the cubic Imice to logarithmic accuracy. The significance of this result to the validily of polymer models is also discussed.

UR - http://www.scopus.com/inward/record.url?scp=36149030578&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36149030578&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/27/18/030

DO - 10.1088/0305-4470/27/18/030

M3 - Article

VL - 27

SP - 6231

EP - 6236

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 18

ER -