### Abstract

For a lattice polymer on the cubic lattice in three dimensional space, it is proved that a single polymer chain is contained in a small volume with probability 1 for negative real z, the measure of the strength of the intrachain interaction, when the polymer length becomes infinite with z being kept finite. The result suggests that the radii of convergence of the perturbation series so far obtained for a chain of finite length N are of order N^{-1/2}.

Original language | English (US) |
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Pages (from-to) | 787-793 |

Number of pages | 7 |

Journal | Journal of the Physical Society of Japan |

Volume | 41 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 1976 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**On the Divergence of the Perturbation Series for the Excluded-Volume Problem in Polymers. II. Collapse of a Single Chain in Poor Solvents.** / Oono, Yoshitsugu.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - On the Divergence of the Perturbation Series for the Excluded-Volume Problem in Polymers. II. Collapse of a Single Chain in Poor Solvents

AU - Oono, Yoshitsugu

PY - 1976/1/1

Y1 - 1976/1/1

N2 - For a lattice polymer on the cubic lattice in three dimensional space, it is proved that a single polymer chain is contained in a small volume with probability 1 for negative real z, the measure of the strength of the intrachain interaction, when the polymer length becomes infinite with z being kept finite. The result suggests that the radii of convergence of the perturbation series so far obtained for a chain of finite length N are of order N-1/2.

AB - For a lattice polymer on the cubic lattice in three dimensional space, it is proved that a single polymer chain is contained in a small volume with probability 1 for negative real z, the measure of the strength of the intrachain interaction, when the polymer length becomes infinite with z being kept finite. The result suggests that the radii of convergence of the perturbation series so far obtained for a chain of finite length N are of order N-1/2.

UR - http://www.scopus.com/inward/record.url?scp=0007420685&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0007420685&partnerID=8YFLogxK

U2 - 10.1143/JPSJ.41.787

DO - 10.1143/JPSJ.41.787

M3 - Article

AN - SCOPUS:0007420685

VL - 41

SP - 787

EP - 793

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 3

ER -