Universality of the optimal path in the strong disorder limit.
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 approximately r (d(opt) ) with d(opt) =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 d(opt) is universal, depending only on the dimension of the system.
Buldyrev
Sergey V
SV
Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
Havlin
Shlomo
S
López
Eduardo
E
Stanley
H Eugene
HE