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The external field effect on the opinion formation based on the majority rule and the q-voter models on the complete graph

Author

Listed:
  • Azhari

    (Department of Physics, Universitas Sumatera Utara, Jl. Dr. T Mansyur, Padang Bulan, Medan City 20155, Indonesia)

  • Roni Muslim

    (Research Center for Quantum Physics, National Research and Innovation Agency (BRIN), South Tangerang 15314, Indonesia3Pesantren Fisika, Hikmah Teknosains Foundation, Yogyakarta 55281, Indonesia)

Abstract

We investigate the external field effect on opinion formation based on the majority rule and q-voter models on a complete graph. The external field can be considered as the mass media in the social system, with the probability p agents following the mass media opinion. Based on our Monte Carlo simulation, the mass media effect is not strong enough to make the system reach a homogeneous state (complete consensus) with the magnetization m=1 for all values of p, indicating the existence of a usual phase transition for all values of p. In the q-voter model, the mass media eliminates the usual phase transition at p≈0.21. We obtain the model’s critical point and scaling parameters using the finite-size scaling analysis and obtain that both models have the same scaling parameters. The external field effect decreases both models’ relaxation time and the relaxation time following the power-law relation such as τ∼Nβ, where N is the population size and β depends on the probability p. In the majority rule model, β follows a linear relation, and in the q-voter model, β follows a power-law relation.

Suggested Citation

  • Azhari & Roni Muslim, 2023. "The external field effect on the opinion formation based on the majority rule and the q-voter models on the complete graph," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 34(07), pages 1-14, July.
  • Handle: RePEc:wsi:ijmpcx:v:34:y:2023:i:07:n:s0129183123500882
    DOI: 10.1142/S0129183123500882
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    Cited by:

    1. Muslim, Roni & NQZ, Rinto Anugraha & Khalif, Muhammad Ardhi, 2024. "Mass media and its impact on opinion dynamics of the nonlinear q-voter model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).

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