Griffiths phases on complex networks

Miguel A. Muñoz, Róbert Juhász, Claudio Castellano, Géza Ódor

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Abstract

Quenched disorder is known to play a relevant role in dynamical processes and phase transitions. Its effects on the dynamics of complex networks have hardly been studied. Aimed at filling this gap, we analyze the contact process, i.e., the simplest propagation model, with quenched disorder on complex networks. We find Griffiths phases and other rare-region effects, leading rather generically to anomalously slow (algebraic, logarithmic,...) relaxation, on Erdos-Rényi networks. Similar effects are predicted to exist for other topologies with a finite percolation threshold. More surprisingly, we find that Griffiths phases can also emerge in the absence of quenched disorder, as a consequence of topological heterogeneity in networks with finite topological dimension. These results have a broad spectrum of implications for propagation phenomena and other dynamical processes on networks.

Original languageEnglish
Article number128701
JournalPhysical review letters
Volume105
Issue number12
DOIs
Publication statusPublished - Sep 17 2010

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ASJC Scopus subject areas

  • Physics and Astronomy(all)

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