MINIMAL PATH ON THE HIERARCHICAL DIAMOND LATTICE
Physics and Astronomy
We consider the minimal paths on a hierarchical diamond lattice, where bonds are assigned a random weight. Depending on the initial distribution of weights, we find all possible asymptotic scaling properties. The different cases found are the small-disorder case, the analog of Levy's distributions with a power-law decay at -infinity, and finally a limit of large disorder which can be identified as a percolation problem. The asymptotic shape of the stable distributions of weights of the minimal path are obtained, as well as their scaling properties. As a side result, we obtain the asymptotic form of the distribution of effective percolation thresholds for finite-size hierarchical lattices.
JOURNAL OF STATISTICAL PHYSICS
(1991). MINIMAL PATH ON THE HIERARCHICAL DIAMOND LATTICE. JOURNAL OF STATISTICAL PHYSICS, 65(40910), 183-204.
Available at: http://aquila.usm.edu/fac_pubs/7105