Title

Minimal Path on the Hierarchical Diamond Lattice

Document Type

Article

Publication Date

10-1-1991

Department

Physics and Astronomy

Abstract

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.

Publication Title

Journal of Statistical Physics

Volume

65

Issue

40910

First Page

183

Last Page

204