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Self-avoiding paths on the pre-Sierpinski gasket
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  • Published: March 1990

Self-avoiding paths on the pre-Sierpinski gasket

  • Kumiko Hattori1,
  • Tetsuya Hattori1,2 &
  • Shigeo Kusuoka3 

Probability Theory and Related Fields volume 84, pages 1–26 (1990)Cite this article

Summary

We study a statistical mechanics of self-avoiding paths on the pre-Sierpinski gasket. We first show the existence of the thermodynamic limit of the (appropriately scaled) free energy. Then we show that there are two domains in the weight parameters (i.e. two phases) between which the scaling differs; i.e. there is a certain kind of phase transition in our model, and we find the critical exponents of the free energy at the phase transition point. We also show the convergence of the distribution of the scaled length of the paths at thermodynamic limit.

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References

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Author information

Authors and Affiliations

  1. Faculty of Science, Gakushuin University, 171, Tokyo, Japan

    Kumiko Hattori & Tetsuya Hattori

  2. Faculty of Engineering, Utsunomiya University, Ishii-cho, 321, Utsunomiya, Japan

    Tetsuya Hattori

  3. Research Institute for Mathematical Sciences, Kyoto University, 606, Kyoto, Japan

    Shigeo Kusuoka

Authors
  1. Kumiko Hattori
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  2. Tetsuya Hattori
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  3. Shigeo Kusuoka
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Cite this article

Hattori, K., Hattori, T. & Kusuoka, S. Self-avoiding paths on the pre-Sierpinski gasket. Probab. Th. Rel. Fields 84, 1–26 (1990). https://doi.org/10.1007/BF01288555

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  • Received: 18 January 1989

  • Issue Date: March 1990

  • DOI: https://doi.org/10.1007/BF01288555

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Keywords

  • Phase Transition
  • Free Energy
  • Stochastic Process
  • Probability Theory
  • Statistical Mechanic
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