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  • Open Access

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

Fabio van Dissel*

Tuan Minh Pham†

Wout Merbis‡

  • Dutch Institute for Emergent Phenomena, Netherlands, Institute for Theoretical Physics, University of Amsterdam, Department of Mathematics, VU Amsterdam, and Centraal Bureau voor de Statistiek, Henri Faasdreef 312, The Hague, The Netherlands

  • *Contact author: fvdissel@ifae.es
  • †Contact author: m.t.pham@uva.nl
  • ‡Contact author: w.merbis@uva.nl
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Phys. Rev. Research 8, 033202 – Published 18 August, 2026

DOI: https://doi.org/10.1103/4qgg-wz64

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 that 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 Z2 symmetry breaking and similar exponent ratios, the full set of critical exponents does not match any known universality class.

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Phys. Rev. Research 8, 033202– Published 18 August, 2026
  • Received 23 February 2026
  • Accepted 8 July 2026
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