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

Author:

Azhari 1,Muslim Roni23

Affiliation:

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

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

3. Pesantren Fisika, Hikmah Teknosains Foundation, Yogyakarta 55281, Indonesia

Abstract

We investigate the external field effect on opinion formation based on the majority rule and [Formula: see text]-voter models on a complete graph. The external field can be considered as the mass media in the social system, with the probability [Formula: see text] 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 [Formula: see text] for all values of [Formula: see text], indicating the existence of a usual phase transition for all values of [Formula: see text]. In the [Formula: see text]-voter model, the mass media eliminates the usual phase transition at [Formula: see text]. 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 [Formula: see text], where [Formula: see text] is the population size and [Formula: see text] depends on the probability [Formula: see text]. In the majority rule model, [Formula: see text] follows a linear relation, and in the q-voter model, [Formula: see text] follows a power-law relation.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Computational Theory and Mathematics,Computer Science Applications,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics

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1. Independence role in the generalized Sznajd model;Physica A: Statistical Mechanics and its Applications;2024-10

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