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Competition between long-range and short-range interactions in the voter model for opinion dynamics

Author

Listed:
  • Jacopo A. Garofalo

    (University of Campania “Luigi Vanvitelli”)

  • Eugenio Lippiello

    (University of Campania “Luigi Vanvitelli”)

  • Fabrizio Rippa

    (University of Campania “Luigi Vanvitelli”)

Abstract

The voter model is a widely used framework in sociophysics to model opinion formation based on local interactions between individuals. In this work, we investigate how the spread of consensus is affected by introducing long-range interactions. Specifically, we study a one-dimensional voter model where a fraction $$\gamma $$ γ of links connect individuals at distances r drawn from a distribution decaying as $$r^{-\sigma -1}$$ r - σ - 1 . Our results reveal that even a small fraction of long-range interactions fundamentally alters the system’s asymptotic behavior. When long-range interactions decay rapidly $$\sigma > 2$$ σ > 2 , their influence is restricted to distances beyond a time-dependent threshold, $$r^*(t)$$ r ∗ ( t ) . For $$r r^*(t)$$ r > r ∗ ( t ) , the correlation function transitions to a power-law decay, $$r^{-\sigma -1}$$ r - σ - 1 , highlighting the capacity of long-range links to propagate consensus across greater distances. When long-range interactions decay more slowly ( $$\sigma

Suggested Citation

  • Jacopo A. Garofalo & Eugenio Lippiello & Fabrizio Rippa, 2025. "Competition between long-range and short-range interactions in the voter model for opinion dynamics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 98(3), pages 1-11, March.
    • Handle: RePEc:spr:eurphb:v:98:y:2025:i:3:d:10.1140_epjb_s10051-025-00900-x
    DOI: 10.1140/epjb/s10051-025-00900-x
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    References listed on IDEAS

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    1. Cannas, Sergio A & Stariolo, Daniel A & Tamarit, Francisco A, 2001. "Dynamics of ferromagnetic spherical spin models with power law interactions: exact solution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 294(3), pages 362-374.
    2. Cugliandolo, Leticia F., 2010. "Topics in coarsening phenomena," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(20), pages 4360-4373.
    3. Hossein Noorazar & Kevin R. Vixie & Arghavan Talebanpour & Yunfeng Hu, 2020. "From classical to modern opinion dynamics," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 31(07), pages 1-60, July.
    4. Galam, Serge, 1999. "Application of statistical physics to politics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 274(1), pages 132-139.
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