Incomplete ordering of the voter model on small-world networks

Details Incomplete ordering of the voter model on small-world networks Incomplete ordering of the voter model on small-world networks

2002-10-21

arxiv.org/abs/cond-mat/0210465v2

Europhys. Lett. 63, 153 (2003)

Physics

Condensed Matter

Statistical Mechanics

6 pages, 3 figures, published version

Scientific paper

10.1209/epl/i2003-00490-0

We investigate how the topology of small-world networks affects the dynamics of the voter model for opinion formation. We show that, contrary to what occurs on regular topologies with local interactions, the voter model on small-world networks does not display the emergence of complete order in the thermodynamic limit. The system settles in a stationary state with coexisting opinions whose lifetime diverges with the system size. Hence the nontrivial connectivity pattern leads to the counterintuitive conclusion that long-range connections inhibit the ordering process. However, for networks of finite size, for which full uniformity is reached, the ordering process takes a time shorter than on a regular lattice of the same size.

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