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A multifractal scale-free lattice

Author

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  • Corso, G.
  • Freitas, J.E.
  • Lucena, L.S.

Abstract

We study the distribution of number of neighbors, ζ, of a multifractal self-affine lattice, Qmf, defined by a single parameter ρ. ζ is neither a constant like in regular lattices nor follows a Gaussian distribution as in the Voronoi lattice. The histogram of ζ show exponential behavior for low ζ and power-law for high ζ. There is no trivial correlation between the distribution of ζ and the critical exponent related to the correlation length, ν, for percolation in the Qmf. The analysis of maximal ζ versus ρ makes evident the relationship between Qmf and the square lattice.

Suggested Citation

  • Corso, G. & Freitas, J.E. & Lucena, L.S., 2004. "A multifractal scale-free lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(1), pages 214-220.
    • Handle: RePEc:eee:phsmap:v:342:y:2004:i:1:p:214-220
    DOI: 10.1016/j.physa.2004.04.081
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