Scaling behaviors of branched polymers

Hajime Aoki, Satoshi Iso, Hikaru Kawai, and Yoshihisa Kitazawa
Phys. Rev. E 62, 6260 – Published 1 November 2000
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Abstract

We study the thermodynamic behavior of branched polymers. We first study random walks in order to clarify the thermodynamic relation between the canonical ensemble and the grand canonical ensemble. We then show that correlation functions for branched polymers are given by those for φ3 theory with a single mass insertion, not those for the φ3 theory themselves. In particular, the two-point function behaves as 1/p4, not as 1/p2, in the scaling region. This behavior is consistent with the fact that the Hausdorff dimension of the branched polymer is 4. In the appendixes we derive the exact two-point correlation function at finite (but large) system size N, which is consistent with the analysis in the body of the paper.

  • Received 8 May 2000

DOI:https://doi.org/10.1103/PhysRevE.62.6260

©2000 American Physical Society

Authors & Affiliations

Hajime Aoki1,*, Satoshi Iso2,†, Hikaru Kawai3,‡, and Yoshihisa Kitazawa2,§

  • 1Department of Physics, Saga University, Saga 840-8502, Japan
  • 2High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305, Japan
  • 3Department of Physics, Kyoto University, Kyoto 606-8502, Japan

  • *Email address: haoki@cc.saga-u.ac.jp
  • Email address: satoshi.iso@kek.jp
  • Email address: hkawai@gauge.scphys.kyoto-u.ac.jp
  • §Email address: kitazawa@post.kek.jp

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Issue

Vol. 62, Iss. 5 — November 2000

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