中国物理B ›› 1997, Vol. 6 ›› Issue (4): 257-265.doi: 10.1088/1004-423X/6/4/003

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RENORMALIZATION GROUP APPROACH TO THE BOND PERCOLATION ON SIERPINSKI CARPETS

秦勇1, 杨展如2, 林振权3   

  1. (1)Department of Physics and Institute of Theoretical Physics, Beijing Normal University, Beijing 100875,China; (2)Department of Physics and Institute of Theoretical Physics, Beijing Normal University, Beijing 100875,China; CCAST(World Laboratory),Beijing 100080,China; (3)Department of Physics, Wenzhou Teachers College, Wenzhou 325003,China; Department of Physics and Institute of Theoretical Physics, Beijing Normal University, Beijing 100875,China
  • 收稿日期:1996-08-13 出版日期:1997-04-20 发布日期:1997-04-20
  • 基金资助:
    Project partly supported by the National Basic Research Project "Nonlinear Science" and the National Natural Science Foundation of China.

RENORMALIZATION GROUP APPROACH TO THE BOND PERCOLATION ON SIERPINSKI CARPETS

LIN ZHEN-QUAN (林振权)ab, YANG ZHAN-RU (杨展如)bc, QIN YONG (秦勇)b   

  1. a Department of Physics, Wenzhou Teachers College, Wenzhou 325003,China; b Department of Physics and Institute of Theoretical Physics, Beijing Normal University, Beijing 100875, China; c CCAST(World Laboratory), Beijing 100080, China
  • Received:1996-08-13 Online:1997-04-20 Published:1997-04-20
  • Supported by:
    Project partly supported by the National Basic Research Project "Nonlinear Science" and the National Natural Science Foundation of China.

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摘要： The critical behaviors of bond percolation on a family of Sierpinski carpets (SCs) are studied. We distinguish two sorts of bonds and assign them to two kinds of occupation probabilities. We develop the usual choice of cell on translationally invariant lattices and choose suitable cells to cover the fractal lattice. On this basis we construct a new real-space renormalization group (RG) transformation scheme and use it to solve the percolation problems. Phase transitions of percolation on such fractals with infinite order of ramification are found at non-trivial bond occupation probabilities. The percolation threshold values, correlation length exponents ν, and the RG flow diagrams are obtained. The flow diagrams are remarkably similar to those of Ising model and Potts model. This agrees with the correspondence between the pure bond percolation and Potts model.

Abstract: The critical behaviors of bond percolation on a family of Sierpinski carpets (SCs) are studied. We distinguish two sorts of bonds and assign them to two kinds of occupation probabilities. We develop the usual choice of cell on translationally invariant lattices and choose suitable cells to cover the fractal lattice. On this basis we construct a new real-space renormalization group (RG) transformation scheme and use it to solve the percolation problems. Phase transitions of percolation on such fractals with infinite order of ramification are found at non-trivial bond occupation probabilities. The percolation threshold values, correlation length exponents $\nu$, and the RG flow diagrams are obtained. The flow diagrams are remarkably similar to those of Ising model and Potts model. This agrees with the correspondence between the pure bond percolation and Potts model.

中图分类号:  (Lattice theory and statistics)

  • 05.50.+q
05.45.Df (Fractals) 05.10.Cc (Renormalization group methods) 05.70.Fh (Phase transitions: general studies)