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

Azhari and Roni Muslim
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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

International Journal of Modern Physics C (IJMPC), 2023, vol. 34, issue 07, 1-14

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.

Keywords: Opinion dynamics; Monte Carlo simulation; external field; relaxation time; phase transition (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0129183123500882

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