Testing the Collective Properties of Small-World Networks through Roughness Scaling

Details Testing the Collective Properties of Small-World Networks through Roughness Scaling Testing the Collective Properties of Small-World Networks through Roughness Scaling

2003-09-08

arxiv.org/abs/cond-mat/0309196v1

Phys. Rev. Lett. 92, 108701 (2004).

Physics

Condensed Matter

Statistical Mechanics

4 pages, 3 figures

Scientific paper

10.1103/PhysRevLett.92.108701

Motivated by a fundamental synchronization problem in scalable parallel computing and by a recent criterion for ``mean-field'' synchronizability in interacting systems, we study the Edwards-Wilkinson model on two variations of a small-worldnetwork. In the first version each site has exactly one random link of strength $p$, while in the second one each site on average has $p$ links of unit strength. We construct a perturbative description for the width of the stationary-state surface (a measure of synchronization), in the weak- and sparse-coupling limits, respectively, and verify the results by performing exact numerical diagonalization. The width remains finite in both cases, but exhibits anomalous scaling with $p$ in the latter for $d\leq 2$.

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