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A thermodynamic counterpart of the Axelrod model of social influence: The one-dimensional case

Author

Listed:
  • Gandica, Y.
  • Medina, E.
  • Bonalde, I.

Abstract

We propose a thermodynamic version of the Axelrod model of social influence. In one-dimensional (1D) lattices, the thermodynamic model becomes a coupled Potts model with a bonding interaction that increases with the site matching traits. We analytically calculate thermodynamic and critical properties for a 1D system and show that an order–disorder phase transition only occurs at T=0 independent of the number of cultural traits q and features F. The 1D thermodynamic Axelrod model belongs to the same universality class of the Ising and Potts models, notwithstanding the increase of the internal dimension of the local degree of freedom and the state-dependent bonding interaction. We suggest a unifying proposal to compare exponents across different discrete 1D models. The comparison with our Hamiltonian description reveals that in the thermodynamic limit the original out-of-equilibrium 1D Axelrod model with noise behaves like an ordinary thermodynamic 1D interacting particle system.

Suggested Citation

  • Gandica, Y. & Medina, E. & Bonalde, I., 2013. "A thermodynamic counterpart of the Axelrod model of social influence: The one-dimensional case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6561-6570.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:24:p:6561-6570
    DOI: 10.1016/j.physa.2013.08.033
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    Cited by:

    1. 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.

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