We employ an agent-based model for cultural dynamics to investigate the effects of spatial heterogeneities on the collective behavior of a social system. We introduce heterogeneity as a random distribution of defects or imperfections in a two-dimensional lattice. Two types of defects are considered separately: obstacles that represent geographic features, and opinion leaders, described as agents exerting unidirectional influence on other agents. In both cases, we characterize two collective phases on the space of parameters of the system, given by the density of defects and a quantity expressing the number of available states: one ordered phase, consisting of a large homogeneous group; and a disordered phase, where many small cultural groups coexist. In the case of leaders, the homogeneous state corresponds to their state. We find that a high enough density of obstacles contributes to cultural diversity in the system. On the other hand, we find a nontrivial effect when opinion leaders are distributed in the system: if their density is greater than some threshold value, leaders are no longer efficient in imposing their state to the population, but they actually promote multiculturality. In this situation, we uncover that leaders, as well as obstacles, serve as locations for the formation of boundaries and segregation between different cultural groups. Moreover, a lower density of leaders than obstacles is needed to induce multiculturality in the system.
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