Volume 69, Number 2, January 2005
|Page(s)||228 - 234|
|Section||Condensed matter: structure, mechanical and thermal properties|
|Published online||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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.