The number and size of branched polymers in high dimensions

Takashi Hara, Gordon Slade

研究成果: Contribution to journalArticle査読

23 被引用数 (Scopus)

抄録

We consider two models of branched polymers (lattice trees) on the d-dimensional hypercubic lattice: (i)the nearest-neighbor model in sufficiently high dimensions, and (ii) a "spread-out" or long-range model for d>8, in which trees are constructed from bonds of length less than or equal to a large parameter L. We prove that for either model the critical exponent θ for the number of branched polymers exists and equals 5/2, and that the critical exponent v for the radius of gyration exists and equals 1/4. This improves our earlier results for the corresponding generating functions. The proof uses the lace expansion, together with an analysis involving fractional derivatives which has been applied previously to the self-avoiding walk in a similar context.

本文言語英語
ページ(範囲)1009-1038
ページ数30
ジャーナルJournal of Statistical Physics
67
5-6
DOI
出版ステータス出版済み - 6 1992
外部発表はい

All Science Journal Classification (ASJC) codes

  • 統計物理学および非線形物理学
  • 数理物理学

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