2002/09/30 by Federico Vázquez, F. Vazquez, P. L. Krapivsky +1 · 1 citation
Physics and Astronomy · #Complex Network Analysis Techniques #Opinion Dynamics and Social Influence #Quantum many-body systems #cond-mat.stat-mech
paper · pdf · doi:10.1088/0305-4470/36/3/103
published as J. Phys. A 36, L61-68 (2003). · 4 pages, 6 figures, 2-column revtex4 format, for submission to J. Phys. A. Revision contains lots of stylistic changes and 1 new result; the main conclusions are the same
arxiv created 2002/11/04 · openalex publication_date 2003/01/08 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
We study opinion formation in a population of leftists, centrists and rightist. In an interaction between neighbouring agents, a centrist and a leftist can become both centrists or leftists (and similarly for a centrist and a rightist), while leftists and rightists do not affect each other. The evolution is controlled by the initial density of centrists ρ 0 . For any spatial dimension the system reaches a centrist consensus with probability ρ 0 , while with probability 1 − ρ 0 the final state is either an extremist consensus, or a frozen population of leftists and rightists. In one dimension, we determine the opinion evolution by mapping the system onto a spin-1 Ising model with zero-temperature Glauber kinetics. The approach to the final state is governed by a t −ψ long-time tail, with ψ → 2ρ 0 /π as ρ 0 → 0. In the one-dimensional frozen state, the length distribution of single-opinion domains has an algebraic small-size tail x −2(1−ψ) and the average domain length is L 2ψ , where L is the length of the system.