Comfort-driven mobility produces spatial fragmentation in Axelrod's model

Axelrod's model for the dissemination of culture combines two key ingredients of social dynamics: social influence, through which people become more similar when they interact, and homophily, which is the tendency of individuals to interact preferentially with similar others. In Axelrod's model, the agents are fixed to the nodes of a network and are allowed to interact with a predetermined set of peers only, resulting in the frustration of a large number of agents that end up culturally isolated. Here we modify this model by allowing the agents to move away from their cultural opposites and stay put when near their cultural likes. The comfort, i.e. the tendency of an agent to stay put in a neighborhood, is determined by the cultural similarity with its neighbors. The less the comfort, the higher the odds that the agents will move apart a fixed step size. We find that the comfort-driven mobility fragments severely the influence network for low initial cultural diversity, resulting in a network composed of only microscopic components in the thermodynamic limit. For high initial cultural diversity and intermediate values of the step size, we find that a macroscopic component coexists with the microscopic ones. The transition between these two fragmentation regimes changes from continuous to discontinuous as the step size increases. In addition, we find that for both very small and very large step sizes the influence network is severely fragmented.