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Phys. Rev. E 70, 035102(R) (2004) [4 pages]

Universality of the optimal path in the strong disorder limit

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Sergey V. Buldyrev1,*, Shlomo Havlin1,2, Eduardo López1, and H. Eugene Stanley1
1Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA
2Minerva Center and Department of Physics, Bar-Ilan University, 52900 Ramat-Gan, Israel

Received 10 February 2004; published 14 September 2004

We study numerically the optimal paths in two and three dimensions on various disordered lattices in the limit of strong disorder. We find that the length ℓ of the optimal path scales with geometric distance r, as ℓ∼rdopt with dopt=1.22±0.01 for d=2 and 1.44±0.02 for d=3, independent of whether the optimization is on a path of weighted bonds or sites, and independent of the lattice or its coordination number. Our finding suggests that the exponent dopt is universal, depending only on the dimension of the system.

© 2004 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevE.70.035102
DOI:
10.1103/PhysRevE.70.035102
PACS:
89.75.Hc

*Current address: Physics Department, Yeshiva University, 500 W. 185 Street, New York, NY 10033.

 
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