Abstract
We consider the voter model dynamics in random networks with anarbitrary distribution of the degree of the nodes. We find thatfor the usual node-update dynamics the average magnetization isnot conserved, while an average magnetization weighted by thedegree of the node is conserved. However, for a link-updatedynamics the average magnetization is still conserved. For theparticular case of a Barabási-Albert scale-free network, thevoter model dynamics leads to a partially ordered metastablestate with a finite-size survival time. This characteristic timescales linearly with system size only when the updating rulerespects the conservation law of the average magnetization. Thisscaling identifies a universal or generic property of the votermodel dynamics associated with the conservation law of themagnetization.
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