Comparison of voter and Glauber ordering dynamics on networks

Details Comparison of voter and Glauber ordering dynamics on networks Comparison of voter and Glauber ordering dynamics on networks

2005-01-25

arxiv.org/abs/cond-mat/0501599v1

Phys. Rev. E 71, 066107 (2005)

Physics

Condensed Matter

Statistical Mechanics

12 pages, 12 figures

Scientific paper

10.1103/PhysRevE.71.066107

We study numerically the ordering process of two very simple dynamical models for a two-state variable on several topologies with increasing levels of heterogeneity in the degree distribution. We find that the zero-temperature Glauber dynamics for the Ising model may get trapped in sets of partially ordered metastable states even for finite system size, and this becomes more probable as the size increases. Voter dynamics instead always converges to full order on finite networks, even if this does not occur via coherent growth of domains. The time needed for order to be reached diverges with the system size. In both cases the ordering process is rather insensitive to the variation of the degreee distribution from sharply peaked to scale-free.

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