Renormalization Group Solution of the Chutes&Ladder Model Open Access

Ball, Lauren Ashley (2014)

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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 bias of the system. We compare these results with similar findings of unconventional phase behavior in hierarchical networks, as well as with related systems involving Levy-distributed backjumps.

Table of Contents

Table of Contents

1. Introduction

1.1 Introduction to scaling behavior and universality

1.2 Background of Rrenormalization Group

1.3 Motivation

2. Network Design

3. Renormalization Group Analysis

4. Conclusion

5. References

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