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

Kozma, B.; Hastings, M. B.; Korniss, G.

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

Authors

Kozma, B.

Hastings, M. B.

Korniss, G.

Description

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 $d\leq 2$.
4 pages, 3 figures