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Role of dimensionality in Axelrod's model for the dissemination of culture

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  • Klemm, Konstantin
  • Eguı́luz, Vı́ctor M
  • Toral, Raúl
  • Miguel, Maxi San

Abstract

We analyze a model of social interaction in one- and two-dimensional lattices for a moderate number of features. We introduce an order parameter as a function of the overlap between neighboring sites. In a one-dimensional chain, we observe that the dynamics is consistent with a second-order transition, where the order parameter changes continuously and the average domain diverges at the transition point. However, in a two-dimensional lattice the order parameter is discontinuous at the transition point characteristic of a first-order transition between an ordered and a disordered state.

Suggested Citation

  • Klemm, Konstantin & Eguı́luz, Vı́ctor M & Toral, Raúl & Miguel, Maxi San, 2003. "Role of dimensionality in Axelrod's model for the dissemination of culture," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 327(1), pages 1-5.
    • Handle: RePEc:eee:phsmap:v:327:y:2003:i:1:p:1-5
    DOI: 10.1016/S0378-4371(03)00428-X
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    Citations

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    Cited by:

    1. Yi-Ling, Wang & Gui-Qing, Zhang, 2013. "Optimal convergence in fame game with familiarity," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 222-226.
    2. Kazuya Yamamoto, 2015. "Mobilization, Flexibility of Identity, and Ethnic Cleavage," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 18(2), pages 1-8.
    3. Juan Carlos González-Avella & Mario G. Cosenza & Konstantin Klemm & Víctor M. Eguíluz & Maxi San Miguel, 2007. "Information Feedback and Mass Media Effects in Cultural Dynamics," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 10(3), pages 1-9.
    4. Reia, Sandro M. & Neves, Ubiraci P.C., 2015. "Activity of a social dynamics model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 435(C), pages 36-43.
    5. Gomes, P.F. & Fernandes, H.A. & Costa, A.A., 2022. "Topological transition in a coupled dynamics in random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
    6. Raducha, Tomasz & Gubiec, Tomasz, 2017. "Coevolving complex networks in the model of social interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 427-435.
    7. Klemm, Konstantin & Eguiluz, Victor M. & Toral, Raul & Miguel, Maxi San, 2005. "Globalization, polarization and cultural drift," Journal of Economic Dynamics and Control, Elsevier, vol. 29(1-2), pages 321-334, January.

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    Keywords

    Non-equilibrium transition; Sociophysics;

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