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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

Azhari

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

E-mail Address: [email protected]

Corresponding author.

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and

Roni Muslim

Research Center for Quantum Physics, National Research and Innovation Agency (BRIN), South Tangerang 15314, Indonesia

Pesantren Fisika, Hikmah Teknosains Foundation, Yogyakarta 55281, Indonesia

E-mail Address: [email protected]

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https://doi.org/10.1142/S0129183123500882Cited by:8 (Source: Crossref)

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 $p \approx 0.21$ . 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 $τ \sim N^{β}$ , 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:

PACS: 89.65.−s, 75.10.Pq, 89.75.Da, 89.75.−k, 05.70.Fh, 05.10.Ln

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