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Phase transition and universality of the three-one spin interaction based on the majority-rule model

Author

Listed:
  • Roni Muslim

    (Department of Physics, Universitas Gadjah Mada, Bulaksumur, Yogyakarta 55281, Indonesia)

  • Rinto Anugraha

    (Department of Physics, Universitas Gadjah Mada, Bulaksumur, Yogyakarta 55281, Indonesia)

  • Sholihun Sholihun

    (Department of Physics, Universitas Gadjah Mada, Bulaksumur, Yogyakarta 55281, Indonesia)

  • Muhammad Farchani Rosyid

    (Department of Physics, Universitas Gadjah Mada, Bulaksumur, Yogyakarta 55281, Indonesia)

Abstract

In this work, we study the opinion dynamics of majority-rule model on a complete graph with additional social behavior namely anticonformity. We consider four spins with three-one interaction; three spins persuade the fourth spin in the population. We perform analytical and numerical calculations to find the critical behavior of the system. From both, we obtained the agreement results, e.g. the system undergoes a second-order phase transition and the critical point of the system only depends on the population number. In addition, the critical point decays exponentially as the number population increases. For the infinite population, the obtained critical point is 1∕6, which agrees well with that of the previous work. We also obtained the critical exponents β≈0.5,γ≈1, and ν≈2 of the model, thus, the model is in the same universality class with the mean-field Ising.

Suggested Citation

  • Roni Muslim & Rinto Anugraha & Sholihun Sholihun & Muhammad Farchani Rosyid, 2021. "Phase transition and universality of the three-one spin interaction based on the majority-rule model," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 32(09), pages 1-12, September.
    • Handle: RePEc:wsi:ijmpcx:v:32:y:2021:i:09:n:s0129183121501151
    DOI: 10.1142/S0129183121501151
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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).
    2. Muslim, Roni & Wella, Sasfan A. & Nugraha, Ahmad R.T., 2022. "Phase transition in the majority rule model with the nonconformist agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P2).

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