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Phase transitions in social impact models of opinion formation


  • Hołyst, Janusz A.
  • Kacperski, Krzysztof
  • Schweitzer, Frank


We study phase transitions in models of opinion formation which are based on the social impact theory. Two different models are discussed: (i) a cellular-automata-based model of a finite group with a strong leader where persons can change their opinions but not their spatial positions, and (ii) a model with persons treated as active Brownian particles interacting via a communication field. In the first model, two stable phases are possible: a cluster around the leader, and a state of social unification. The transition into the second state occurs for a large leader strength and/or for a high level of social noise. In the second model, we find three stable phases, which correspond either to a “paramagnetic” phase (for high noise and strong diffusion), a “ferromagnetic” phase (for small nose and weak diffusion), or a phase with spatially separated “domains” (for intermediate conditions).

Suggested Citation

  • Hołyst, Janusz A. & Kacperski, Krzysztof & Schweitzer, Frank, 2000. "Phase transitions in social impact models of opinion formation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 285(1), pages 199-210.
  • Handle: RePEc:eee:phsmap:v:285:y:2000:i:1:p:199-210
    DOI: 10.1016/S0378-4371(00)00282-X

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    Cited by:

    1. Yao-feng Zhang & Hong-ye Duan & Zhi-lin Geng, 2017. "Evolutionary Mechanism of Frangibility in Social Consensus System Based on Negative Emotions Spread," Complexity, Hindawi, vol. 2017, pages 1-8, June.
    2. Abdulkadir Abdulrashid Rafindadi & Zarinah Yusof, 2014. "Are the Periods of Currency Collapse an Impediment to Entrepreneurship and Entrepreneurial Haven? Evidence from Regional Comparison," International Journal of Economics and Financial Issues, Econjournals, vol. 4(4), pages 886-908.
    3. Jędrzejewski, Arkadiusz & Sznajd-Weron, Katarzyna, 2018. "Impact of memory on opinion dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 306-315.
    4. Grabowski, Andrzej, 2009. "Opinion formation in a social network: The role of human activity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(6), pages 961-966.
    5. Chakrabarti, Anindya S., 2016. "Cross-correlation patterns in social opinion formation with sequential data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 442-454.
    6. Seungkyu Shin & Juyong Park, 2018. "On-Chart Success Dynamics Of Popular Songs," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 21(03n04), pages 1-18, May.
    7. Schweitzer, Frank & Zimmermann, Jörg & Mühlenbein, Heinz, 2002. "Coordination of decisions in a spatial agent model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 303(1), pages 189-216.
    8. Hang-Hyun Jo & Jeoung-Yoo Kim, 2012. "Competitive Targeted Marketing," ISER Discussion Paper 0834, Institute of Social and Economic Research, Osaka University.
    9. Hutzler, S. & Sommer, C. & Richmond, P., 2016. "On the relationship between income, fertility rates and the state of democracy in society," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 452(C), pages 9-18.
    10. Weimer-Jehle, Wolfgang, 2008. "Cross-impact balances," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3689-3700.
    11. Katarzyna Ostasiewicz & Michal H. Tyc & Piotr Goliczewski & Piotr Magnuszewski & Andrzej Radosz & Jan Sendzimir, 2006. "Integrating economic and psychological insights in binary choice models with social interactions," Papers physics/0609170,
    12. 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.
    13. Yaofeng Zhang & Renbin Xiao, 2015. "Modeling and Simulation of Polarization in Internet Group Opinions Based on Cellular Automata," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-15, August.
    14. Barunik, J. & Vosvrda, M., 2009. "Can a stochastic cusp catastrophe model explain stock market crashes?," Journal of Economic Dynamics and Control, Elsevier, vol. 33(10), pages 1824-1836, October.


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