ISSN:
1572-9613
Keywords:
Percolation clusters
;
self-avoiding walks
;
indefinitely growing self-avoiding walks
;
real-space renormalization group
;
fractals
;
universality
;
corrections to scaling
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract We calculate the average number of stepsN for edge-to-edge, “normal,” and indefinitely growing self-avoiding walks (SAWs) on two-dimensional critical percolation clusters, using the real-space renormalization-group approach, with small “H” cells. Our results are of the formN=AL D SAW+B, whereL is the end-to-end distance. Similarly to several deterministic fractals, the fractal dimensionsD SAW for these three different kinds of SAWs are found to be equal, and the differences between them appear in the amplitudesA and in the correction termsB. This behavior is atributed to the hierarchical nature of the critical percolation cluster.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02183619
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