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Phase transition and universality of the majority-rule model on complex networks

Author

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  • Didi Ahmad Mulya

    (Research Center for Quantum Physics, National Research and Innovation Agency (BRIN), South Tangerang 15314, Indonesia†Department of Industrial Engineering, University of Technology Yogyakarta, Yogyakarta 55285, Indonesia)

  • Roni Muslim

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

Abstract

In this paper, we investigate the phenomena of order-disorder phase transition and the universality of the majority-rule model defined on three complex networks, namely the Barabási–Albert, Watts–Strogatz and Erdős–Rényi networks. Assume each agent holds two possible opinions randomly distributed across the networks’ nodes. Agents adopt anticonformity and independence behaviors, represented by the probability p, where with a probability p, agents adopt anticonformity or independence behavior. Based on our numerical simulation results and finite-size scaling analysis, it is found that the model undergoes a continuous phase transition for all networks, with critical points for the independence model greater than those for the anticonformity model in all three networks. We obtain critical exponents identical to the opinion dynamics model defined on a complete graph, indicating that the model exhibits the same universality class as the mean-field Ising model.

Suggested Citation

  • Didi Ahmad Mulya & Roni Muslim, 2024. "Phase transition and universality of the majority-rule model on complex networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 35(10), pages 1-14, October.
    • Handle: RePEc:wsi:ijmpcx:v:35:y:2024:i:10:n:s0129183124501250
    DOI: 10.1142/S0129183124501250
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