Renormalization Group Solution of the Chutes&Ladder Model
arXiv:1410.2092 · doi:10.1016/j.physa.2014.11.020
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.
7 pages, RevTex4.1; for related information, see http://www.physics.emory.edu/faculty/boettcher/
References in corpus (9)
- Critical phenomena in complex networks
- Small-World Bonds and Patchy Percolation on the Hanoi Network
- Hierarchical, Regular Small-World Networks
- Griffiths singularities and algebraic order in the exact solution of an Ising model on a fractal modular network
- Ising model on the Apollonian network with node dependent interactions
- Anomalous Diffusion on the Hanoi Networks
- Quantum Transport through Hierarchical Structures
- Geometry and Dynamics for Hierarchical Regular Networks
- From explosive to infinite-order transitions on a hyperbolic network