Phase transition in the majority rule model with the nonconformist agents

Muslim, Roni; Wella, Sasfan Arman; Nugraha, Ahmad R. T.

doi:10.1016/j.physa.2022.128307

Cited by 9 publications

(2 citation statements)

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“…The same scaling parameter means that both models are similar in terms of universality class because both models are defined on the same graph, namely a complete graph, even though the two models have different microscopic interactions. However, it is not necessary that if the models are defined on the same graph, they will have the same universality class [39]. The value of this scaling parameter depends on the model's topology, especially the model's network structure.…”

Section: Resultsmentioning

confidence: 99%

“…The value of this scaling parameter depends on the model's topology, especially the model's network structure. For example, the scaling parameters of the model defined on the complete graph will be different from the model defined on the two-dimensional square lattice [39] The interesting quantity in the Monte Carlo simulation is the relaxation time τ , which is the time needed to reach a homogeneous state (all agents at the end have the same opinion). In this part, we want to find the relation of the relaxation time τ to the system size N .…”

Section: Resultsmentioning

confidence: 99%

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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

Muslim²

2022

Int. J. Mod. Phys. C

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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.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%