Symmetric preferences, asymmetric outcomes: Tipping dynamics in an open-city segregation model

Schelling’s model of segregation demonstrates that even in the absence of social or governmental interventions, individuals with mild in-group preferences can self-organize into strongly segregated neighborhoods. Many variants of this celebrated model have been proposed by assuming agents tend to increase their satisfaction. Complementary to this traditional, utility-based approach, we model residential moves using satisfaction-independent reaction rates in a spatially extended chemical reaction network. The resulting model exhibits an emergent phenomenon: despite symmetric in-group preferences, the system undergoes a tipping transition at a critical preference level, beyond which one agent type dominates. We characterize this asymmetric phase transition in details using mean-field analysis, numerical simulations and finite size scaling methods. We find that while the transition shares key features with the Ising universality class, such as ${\mathbb{Z}}_2$ symmetry breaking and similar exponent ratios, the full set of critical exponents does not match any known universality class.