1208.4381 (Y. Gandica et al.)

A thermodynamic counterpart of the Axelrod model of social influence    [PDF]

Y. Gandica, E. Medina, I. Bonalde

We propose a thermodynamic version of the Axelrod model of social influence. In one-dimensional lattices, the thermodynamic model becomes a Potts model of several coupled chains with a site (agent) 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 of the agents. We find that the parameter q does not induce any transition or anomaly in the thermodynamic model, as it does in the standard social model that violates detailed balance. 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 (agent).

View original: http://arxiv.org/abs/1208.4381