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Open Access item Conservation laws for the voter model in complex networks

Authors:Suchecki, Krzysztof
Eguíluz, Víctor M.
San Miguel, Maxi
Keywords:[PACS] Order-disorder transformations; statistical mechanics of model systems, [PACS] Complex systems, [PACS] Dynamics of social systems
Issue Date:15-Jan-2005
Publisher:EDP Sciences
Citation:Europhysics Letters 69, 228-234 (2005)
Abstract:We consider the voter model dynamics in random networks with an arbitrary distribution of the degree of the nodes. We find that for the usual node-update dynamics the average magnetization is not conserved, while an average magnetization weighted by the degree of the node is conserved. However, for a link-update dynamics the average magnetization is still conserved. For the particular case of a Barabasi-Albert scale-free network the voter model dynamics leads to a partially ordered metastable state with a finite size survival time. This characteristic time scales linearly with system size only when the updating rule respects the conservation law of the average magnetization. This scaling identifies a universal or generic property of the voter model dynamics associated with the conservation law of the magnetization.
Description:7 pages, 4 figures.-- PACS nrs.: 64.60.Cn, 89.75.-k, 87.23.Ge.-- Pre-print version available at ArXiv: http://arxiv.org/abs/cond-mat/0408101.
Publisher version (URL):http://dx.doi.org/10.1209/epl/i2004-10329-8
URI:http://hdl.handle.net/10261/7473
ISSN:0295-5075
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