Abstract
"Normal" and indefinitely-growing (IG) self-avoiding walks (SAWs) are exactly enumerated on several deterministic fractals (the Manderbrot-Given curve with and without dangling bonds, and the 3-simplex). On the n th fractal generation, of linear size L, the average number of steps behaves asymptotically as 〈N〉=ALDsaw+B. In contrast to SAWs on regular lattices, on these factals IGSAWs and "normal" SAWs have the same fractal dimension Dsaw. However, they have different amplitudes (A) and correction terms (B).
Original language | English |
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Pages (from-to) | 545-563 |
Number of pages | 19 |
Journal | Journal of Statistical Physics |
Volume | 77 |
Issue number | 3-4 |
DOIs | |
State | Published - 1 Nov 1994 |
Externally published | Yes |
Keywords
- Self-avoiding walks
- fractals
- indefinitely-growing self-avoiding walks
- renormalization
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics