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Jacobsen JL, Zinn-Justin P. Monochromatic path crossing exponents and graph connectivity in two-dimensional percolation. Phys Rev E Stat Nonlin Soft Matter Phys. 2002;66(5):055102doi: 10.1103/PhysRevE.66.055102.
Jacobsen, J. L., & Zinn-Justin, P. (2002). Monochromatic path crossing exponents and graph connectivity in two-dimensional percolation. Physical review. E, Statistical, nonlinear, and soft matter physics, 66(5), 055102. https://doi.org/10.1103/PhysRevE.66.055102
Jacobsen, Jesper Lykke, and Zinn-Justin, Paul. "Monochromatic path crossing exponents and graph connectivity in two-dimensional percolation." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 66,5 (2002): 055102. doi: https://doi.org/10.1103/PhysRevE.66.055102
Jacobsen JL, Zinn-Justin P. Monochromatic path crossing exponents and graph connectivity in two-dimensional percolation. Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Nov;66(5):055102. doi: 10.1103/PhysRevE.66.055102. Epub 2002 Nov 19. PMID: 12513543.
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Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Nov;66(5):055102. doi: 10.1103/PhysRevE.66.055102. Epub 2002 Nov 19.

Monochromatic path crossing exponents and graph connectivity in two-dimensional percolation.

Physical review. E, Statistical, nonlinear, and soft matter physics

Jesper Lykke Jacobsen, Paul Zinn-Justin

Affiliations

  1. Laboratoire de Physique Théorique et Modèles Statistiques, Université Paris-Sud, Bâtiment 100, 91405 Orsay Cedex, France. [email protected]

PMID: 12513543 DOI: 10.1103/PhysRevE.66.055102

Abstract

We consider the fractal dimensions d(k) of the k-connected part of percolation clusters in two dimensions, generalizing the cluster (k=1) and backbone (k=2) dimensions. The codimensions x(k)=2-d(k) describe the asymptotic decay of the probabilities P(r,R) approximately (r/R)(x(k)) that an annulus of radii r<<1 and R>>1 is traversed by k disjoint paths, all living on the percolation clusters. Using a transfer matrix approach, we obtain numerical results for x(k), k

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