Europhys. Lett.
Volume 63, Number 1, July 2003
Page(s) 153 - 158
Section Interdisciplinary physics and related areas of science and technology
Published online 01 June 2003
DOI: 10.1209/epl/i2003-00490-0
Europhys. Lett., 63 (1) , pp. 153-158 (2003)

Incomplete ordering of the voter model on small-world networks

C. Castellano1, 2, D. Vilone1 and A. Vespignani3

1  Dipartimento di Fisica, Università di Roma "La Sapienza" P. le A. Moro 2, I-00185 Roma, Italy
2  INFM, Unità di Roma 1 - P. le A. Moro 2, I-00185 Roma, Italy
3  Laboratoire di Physique Théorique (UMR du CNRS 8627) Bâtiment 210 Université de Paris-Sud - 91405 Orsay Cedex, France

(Received 24 October 2002; accepted in final form 2 May 2003)

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.

87.23.Ge - Dynamics of social systems.
89.75.-k - Complex systems.
05.70.Ln - Nonequilibrium and irreversible thermodynamics.

© EDP Sciences 2003