Renormalization Group Solution of the Chutes&Ladder Model
Statistical Mechanics
2015-06-03 v1 Physics and Society
Abstract
We analyze a semi-infinite one-dimensional random walk process with a biased motion that is incremental in one direction and long-range in the other. On a network with a fixed hierarchy of long-range jumps, we find with exact renormalization group calculations that there is a dynamical transition between a localized adsorption phase and an anomalous diffusion phase in which the mean-square displacement exponent depends non-universally on the Bernoulli coin. We relate these results to similar findings of unconventional phase behavior in hierarchical networks.
Cite
@article{arxiv.1410.2092,
title = {Renormalization Group Solution of the Chutes&Ladder Model},
author = {Lauren A. Ball and Alfred C. K. Farris and Stefan Boettcher},
journal= {arXiv preprint arXiv:1410.2092},
year = {2015}
}
Comments
7 pages, RevTex4.1; for related information, see http://www.physics.emory.edu/faculty/boettcher/