Self-Avoiding Walks Between Terminals on Percolation Clusters

  • Liv Furuberg
  • Amnon Aharony
  • Jens Feder
  • Torstein Jøssang
Part of the NATO ASI Series book series (volume 167)


Many natural structures exhibit fractal geometry, and much recent interest has been devoted to studying the physical properties of such structures [1]. In the fractal regime, many of these properties depend on the length scale L via power laws, e.g. X(L) ~ L x . Often, one needs an infinite set of exponents, {x}, in order to fully characterize the structure [1]. We find that the various self-avoiding paths connecting two terminals on a percolating cluster scale with the Euclidean distance between the terminals. The different paths scale with different exponents forming a continuous spectrum.


Fractal Dimension Percolation Threshold Fractal Geometry Terminal Point Opposite Edge 
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Copyright information

© Plenum Press, New York 1987

Authors and Affiliations

  • Liv Furuberg
    • 1
  • Amnon Aharony
    • 1
    • 2
  • Jens Feder
    • 1
  • Torstein Jøssang
    • 1
  1. 1.Institute of PhysicsUniversity of OsloBlindern, Oslo 3Norway
  2. 2.School of Physics and AstronomyTel Aviv UniversityTel AvivIsrael

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