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Exact analysis of the self-avoiding random walks on two infinite families of fractals

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  • Milos̆ević, Sava
  • Z̆ivić, Ivan

Abstract

We introduce two infinite families of fractals that we name the Φ family and the Koch family, according to their first members, which are the plane-filling Φ lattice and the Koch fractal curve, respectively. The fractal dimension df of Φ family varies from 2 to 1 (and from 1.465 to 1, in the case of the Koch family) when the fractal enumerator b (an odd integer) varies from 3 to ∞. We have calculated exactly the critical exponents of the self-avoiding random walks (SAWs) on these fractals. Our results render it possible to perform a complete and exact study of the fractal to Euclidean crossover, which, in this case, occurs when b→∞. It turns out that all critical exponents, when df→1 (b→∞), tend to the corresponding Euclidean values with a unique correction term of the type constant/ln(b).

Suggested Citation

  • Milos̆ević, Sava & Z̆ivić, Ivan, 1992. "Exact analysis of the self-avoiding random walks on two infinite families of fractals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 186(3), pages 329-345.
    • Handle: RePEc:eee:phsmap:v:186:y:1992:i:3:p:329-345
    DOI: 10.1016/0378-4371(92)90205-5
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