Volume 69, Number 2, January 2005
|228 - 234
|Condensed matter: structure, mechanical and thermal properties
|17 December 2004
Conservation laws for the voter model in complex networks
Instituto Mediterráneo de Estudios Avanzados IMEDEA (CSIC-UIB) E-07122 Palma de Mallorca, Spain
Accepted: 8 November 2004
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 Barabási-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.
PACS: 64.60.Cn – Order-disorder transformations; statistical mechanics of model systems / 89.75.-k – Complex systems / 87.23.Ge – Dynamics of social systems
© EDP Sciences, 2005
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