Nonequilibrium Phase Transition in a Model for Social Influence

Abstract

We present extensive numerical simulations of the Axelrod's model for social influence, aimed at understanding the formation of cultural domains. This is a nonequilibrium model with short range interactions and a remarkably rich dynamical behavior. We study the phase diagram of the model and uncover a nonequilibrium phase transition separating an ordered (culturally polarized) phase from a disordered (culturally fragmented) one. The nature of the phase transition can be continuous or discontinuous depending on the model parameters. At the transition, the size of cultural regions is power-law distributed.PACS numbers: 87.23. Ge, 05.50.+q, 05.70.Ln, 84.35.+i Recently, the study of complex systems entered social science in order to understand how self-organization, cooperative effects, and adaptation arise in social systems [1]. In this context the use of simple automata or dynamical models often elucidates the mechanisms at the basis of the observed complex behaviors [1,2].In this spirit, Axelrod has recently proposed an interesting model to mimic how dissemination of culture works [3,4]. Culture is used here to indicate the set of individual attributes, such as "language, art, technical standards and social norms" [1] subject to social influence, i.e., that can be changed as an effect of mutual interactions. The automaton does not consider the effect of central institutions or mass media and focuses on the self-organization resulting from a simple local dynamics representing the social influence. This dynamics is assumed to satisfy two simple properties: (i) individuals are more likely to interact with others who already share many of their cultural attributes; (ii) interaction increases the number of features that individuals share. Starting from an initial state with features distributed randomly this leads to the formation and coarsening of regions of shared culture.In this Letter, we carry out an accurate numerical analysis of Axelrod's model that unravels a remarkably rich behavior, not detected in previous investigations. Depending on the initial degree of disorder, the model undergoes a phase transition separating an ordered from a disordered phase. The ordered phase is characterized by the growth of a dominant cultural region spanning a large fraction of the whole system. On the contrary, in the disordered phase the system freezes in a highly fragmented state with a nontrivial distribution of the sizes of cultural regions. Such a fragmented configuration is reached in a finite time, which diverges at the phase transition. In the whole ordered phase instead, the coarsening process lasts for a time proportional to the system size, before freezing into the culturally polarized state.

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