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Non-monotonic spontaneous magnetization in a Sznajd-like consensus model

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  • Sabatelli, Lorenzo
  • Richmond, Peter

Abstract

Ising or Potts models of ferromagnetism have been widely used to describe locally interacting social or economic systems. We consider a related model, introduced by Sznajd to describe the evolution of consensus in a society. In this model, the opinion or state of any spins can only be changed through the influence of neighbouring pairs of similarly aligned spins. Such pairs can polarize their neighbours. We show that, assuming the global dynamics evolved in a synchronous manner, the two-state Sznajd model exhibits a non-monotonically decreasing overall orientation that has a maximum value when the system is subject to a finite value of noise. Reinterpreting the model in terms of opinions within a society we predict that consensus can be increased by the addition of an appropriate amount of random noise. These features are explained by the presence of islands of complete orientation that are stable in the absence of noise but removed via the presence of added noise.

Suggested Citation

  • Sabatelli, Lorenzo & Richmond, Peter, 2004. "Non-monotonic spontaneous magnetization in a Sznajd-like consensus model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 334(1), pages 274-280.
    • Handle: RePEc:eee:phsmap:v:334:y:2004:i:1:p:274-280
    DOI: 10.1016/j.physa.2003.10.062
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    References listed on IDEAS

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    1. Lorenzo Sabatelli & Peter Richmond, 2003. "Phase Transitions, Memory And Frustration In A Sznajd-Like Model With Synchronous Updating," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 14(09), pages 1223-1229.
    2. Katarzyna Sznajd-Weron & Józef Sznajd, 2000. "Opinion Evolution In Closed Community," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 11(06), pages 1157-1165.
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    Cited by:

    1. Sznajd-Weron, Katarzyna & Sznajd, Józef & Weron, Tomasz, 2021. "A review on the Sznajd model — 20 years after," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    2. Sabatelli, Lorenzo & Richmond, Peter, 2004. "A consensus-based dynamics for market volumes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 62-66.
    3. Gündüç, Semra & Eryiğit, Recep, 2015. "The role of persuasion power on the consensus formation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 426(C), pages 16-24.
    4. Krzysztof Urbanowicz & Peter Richmond & Janusz A. Ho{l}yst, 2014. "A simple model of local prices and associated risk evaluation," Papers 1408.1352, arXiv.org.
    5. Grabowski, A. & Kosiński, R.A., 2006. "Ising-based model of opinion formation in a complex network of interpersonal interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(2), pages 651-664.

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