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

Authors: Yerali Gandica, Ernesto Medina and Ismardo Bonalde.

Ref.: Physica A: Statistical Mechanics and its Applications 392 (24) , pp. 6561-6570 (2013)

Abstract: We propose a thermodynamic version of the Axelrod model of social influence. In onedimensional 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 one-dimensional 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 one-dimensional 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 one dimensional models. The comparison with a Hamiltonian system revealed that the original out-of-equilibrium 1-D Axelrod model with noise, in the thermodynamic, limit behaves like an ordinary thermodynamic one-dimensional interacting particle system.