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

TL;DR

This paper models segregation dynamics using a reaction network approach, revealing a tipping transition where one agent type dominates despite symmetric preferences, with critical behavior akin to but not matching known universality classes.

Contribution

It introduces a reaction network model for segregation dynamics, uncovering a novel tipping transition and detailed critical phenomena analysis.

Findings

Identification of a tipping transition at a critical preference level

System exhibits symmetry breaking similar to Ising model

Critical exponents differ from known universality classes

Abstract

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 a counter-intuitive 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.