Minimal Path on the Hierarchical Diamond Lattice
Physics and Astronomy
Mathematics and Natural Sciences
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 Lévy's distributions with a power-law decay at-∞, 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
da Silva, L. R.,
Lucena, L. S.,
Pandey, R. B.
(1991). Minimal Path on the Hierarchical Diamond Lattice. Journal of Statistical Physics, 65, 183-204.
Available at: https://aquila.usm.edu/fac_pubs/7105