Phase diagram of a Schelling segregation model

TL;DR

This paper applies statistical physics methods to analyze a Schelling segregation model, creating a phase diagram that identifies different regimes and transitions, including sudden ethnic turnovers, and links to physical spin models.

Contribution

It introduces a physics-inspired approach to characterize segregation regimes and transitions in Schelling's model, providing a new framework for socio-economic system analysis.

Findings

Identification of multiple segregation regimes

Quantitative characterization of phase transitions

Links established with spin-1 physics models

Abstract

The collective behavior in a variant of Schelling's segregation model is characterized with methods borrowed from statistical physics, in a context where their relevance was not conspicuous. A measure of segregation based on cluster geometry is defined and several quantities analogous to those used to describe physical lattice models at equilibrium are introduced. This physical approach allows to distinguish quantitatively several regimes and to characterize the transitions between them, leading to the building of a phase diagram. Some of the transitions evoke empirical sudden ethnic turnovers. We also establish links with 'spin-1' models in physics. Our approach provides generic tools to analyze the dynamics of other socio-economic systems.