Studies of cultural differentiation have shown that social mechanisms that normally lead to cultural convergence-homophily and influence-can also explain how distinct cultural groups can form. However, this emergent cultural diversity has proven to be unstable in the face of cultural drift-small errors or innovations that allow cultures to change from within. The authors develop a model of cultural differentiation that combines the traditional mechanisms of homophily and influence with a third mechanism of network homophily, in which network structure co-evolves with cultural interaction. Results show that in certain regions of the parameter space, these co-evolutionary dynamics can lead to patterns of cultural diversity that are stable in the presence of cultural drift. The authors address the implications of these findings for understanding the stability of cultural diversity in the face of increasing technological trends toward globalization.

We study the effect of mass media, modeled as an applied external field, on a social system based on Axelrod's model for the dissemination of culture. The numerical simulations show that the system undergoes a nonequilibrium phase transition between an ordered phase ͑homogeneous culture͒ specified by the mass media and a disordered ͑culturally fragmented͒ one. The critical boundary separating these phases is calculated on the parameter space of the system, given by the intensity of the mass media influence and the number of options per cultural attribute. Counterintuitively, mass media can induce cultural diversity when its intensity is above some threshold value. The nature of the phase transition changes from continuous to discontinuous at some critical value of the number of options. In recent years, the research on complex systems has extended to social science in order to understand how collective behaviors arise in social systems. Several mathematical models, inspired by analogies with physical systems, have been proposed to describe a variety of phenomena occurring in social dynamics ͓1-4͔. Processes such as selforganization, cooperation, epidemic spreading, opinion formation, propagation of information, economic exchanges, and evolution of social structures have been studied by means of discrete-time and discrete-space dynamical systems. In this context, there has been interest in the model introduced by Axelrod ͓5͔ to investigate the dissemination of culture among interacting agents in a social system ͓6-11͔. From the point of view of statistical physics, this model is appealing because it exhibits nontrivial out of equilibrium dynamics, as in other well studied systems with phase ordering properties ͓13͔. Studies of this model have mainly focused on the collective properties that result from the interactions between the elements representing endogenous social influences.In this paper we investigate the effect of external cultural influences such as mass media on a social system. Our approach is based on the adaptive interaction dynamics of Axelrod's model for the dissemination of culture. Agents can interact with their neighbors in the system and with the mass media according to the cultural similarities that they share, in each case. The concept of culture is intended here as a set of individual features or attributes that are subject to social or external influence. The numerical simulations show that, depending on the value of a parameter that represents the intensity of the mass media influence and on the number of options available per cultural attribute, the system displays a phase transition between a specific ordered phase ͑a homogeneous culture͒ imposed by the mass media and a disordered ͑culturally fragmented͒ phase. Surprisingly, mass media can induce cultural diversity when its intensity is above some threshold value. The nature of this transition changes from continuous to discontinuous when the number of options per cultural feature is increased.

A nonequilibrium system of locally interacting elements in a lattice with an absorbing order-disorder phase transition is studied under the effect of additional interacting fields. These fields are shown to produce interesting effects in the collective behavior of this system. Both for autonomous and external fields, disorder grows in the system when the probability of the elements to interact with the field is increased. There exists a threshold value of this probability beyond which the system is always disordered. The domain of parameters of the ordered regime is larger for nonuniform local fields than for spatially uniform fields. However, the zero field limit is discontinous. In the limit of vanishingly small probability of interaction with the field, autonomous or external fields are able to order a system that would fall in a disordered phase under local interactions of the elements alone. We consider different types of fields which are interpreted as forms of mass media acting on a social system in the context of Axelrod's model for cultural dissemination.

We study the coevolution of network structure and node states in a model of multiple state interacting agents. The system displays two transitions, network recombination and fragmentation, governed by time scales that emerge from the dynamics. The recombination transition separates a frozen configuration, composed by disconnected network components whose agents share the same state, from an active configuration, with a fraction of links that are continuously being rewired. The nature of this transition is explained analytically as the maximum of a characteristic time. The fragmentation transition, that appears between two absorbing frozen phases, is an anomalous order-disorder transition, governed by a crossover between the time scales that control the structure and state dynamics.