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Ferromagnetic and spin-glass like transition in the q-neighbor Ising model on random graphs

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  • A. Krawiecki

    (Warsaw University of Technology)

Abstract

The q-neighbor Ising model is investigated on homogeneous random graphs with a fraction of edges associated randomly with antiferromagnetic exchange integrals and the remaining edges with ferromagnetic ones. It is a nonequilibrium model for the opinion formation in which the agents, represented by two-state spins, change their opinions according to a Metropolis-like algorithm taking into account interactions with only a randomly chosen subset of their q neighbors. Depending on the model parameters in Monte Carlo simulations, phase diagrams are observed with first-order ferromagnetic transition, both first- and second-order ferromagnetic transitions and second-order ferromagnetic and spin-glass-like transitions as the temperature and fraction of antiferromagnetic exchange integrals are varied; in the latter case, the obtained phase diagrams qualitatively resemble those for the dilute spin-glass model. Homogeneous mean-field and pair approximations are extended to take into account the effect of the antiferromagnetic exchange interactions on the ferromagnetic phase transition in the model. For a broad range of parameters, critical temperatures for the first- or second-order ferromagnetic transition predicted by the homogeneous pair approximation show quantitative agreement with those obtained from Monte Carlo simulations; significant differences occur mainly in the vicinity of the tricritical point in which the critical lines for the second-order ferromagnetic and spin-glass-like transitions meet. Graphic abstract

Suggested Citation

  • A. Krawiecki, 2021. "Ferromagnetic and spin-glass like transition in the q-neighbor Ising model on random graphs," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(3), pages 1-15, March.
    • Handle: RePEc:spr:eurphb:v:94:y:2021:i:3:d:10.1140_epjb_s10051-021-00084-0
    DOI: 10.1140/epjb/s10051-021-00084-0
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    References listed on IDEAS

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    1. Andrzej Krawiecki, 2018. "Spin-glass-like transition in the majority-vote model with anticonformists," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 91(3), pages 1-7, March.
    2. Andrzej Krawiecki, 2020. "Ferromagnetic and spin-glass-like transition in the majority vote model on complete and random graphs," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 93(9), pages 1-14, September.
    3. Liang Li & Jia-lin Wu & Jin-xiang Ding, 2013. "Analysis of Bank Queueing Based on Operations Research," Springer Books, in: Ershi Qi & Jiang Shen & Runliang Dou (ed.), The 19th International Conference on Industrial Engineering and Engineering Management, edition 127, chapter 0, pages 777-787, Springer.
    4. Bartłomiej Nowak & Katarzyna Sznajd-Weron, 2019. "Homogeneous Symmetrical Threshold Model with Nonconformity: Independence versus Anticonformity," Complexity, Hindawi, vol. 2019, pages 1-14, April.
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