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

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dc.creatorKozma, B.
dc.creatorHastings, M. B.
dc.creatorKorniss, G.
dc.date2003-09-08
dc.date.accessioned2026-07-07T02:53:21Z
dc.date.available2026-07-07T02:53:21Z
dc.descriptionMotivated 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 $d\leq 2$.
dc.description4 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/cond-mat/0309196
dc.identifierhttp://arxiv.org/abs/cond-mat/0309196
dc.identifierPhys. Rev. Lett. 92, 108701 (2004).
dc.identifierdoi:10.1103/PhysRevLett.92.108701
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/22180
dc.subjectStatistical Mechanics
dc.subjectDisordered Systems and Neural Networks
dc.titleTesting the Collective Properties of Small-World Networks through Roughness Scaling
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