Conservation laws for the voter model in complex networks

By K. Suchecki, Víctor M. Eguíluz, M. S. M. Imedea, P. Mallorca, Spain University of Technology, Poland.. 2004

165 citations recorded by the source corpus.

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.

Subfields: Condensed Matter Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0874645a8d48ecf85075b83ae4f05cda193beb6f

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In Condensed Matter Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Statistical physics of social dynamics (2007, background): “Since the WS network for p = 1 is a random network (and then practically an infinite-dimensional system) this is consistent with the observation of the transition also in the mean field approaches (Castellano et al., 2000; Vazquez and Redner, 2007).”
The structure and dynamics of multilayer networks (2014, methodology): “On SF networks with exponent γ , direct voter model makes ⟨T ⟩ to scale as the size N of the network for γ > 3 and sublinearly for γ ≤ 3 [296,305,306].”
Networks beyond pairwise interactions: structure and dynamics (2020, background): “Indeed, in order to maintain the average magnetization of the system, one has to move from the aforementioned node-update rule to a link-update rule [491] (Figs.”
Critical phenomena in complex networks (2007, methodology): “In this model, the evolution of the system on a complex network is qualitatively the same as on high-dimensional regular lattices, and τN ∼ N (Suchecki et al., 2005a,b).”