Eur. Phys. J. B 70, 293-304 (2009)
https://doi.org/10.1140/epjb/e2009-00234-0

Phase diagram of a Schelling segregation model

¹ Laboratoire de Physique Statistique (LPS, UMR 8550 CNRS-ENS-Paris 6-Paris 7), École Normale Supérieure, Paris, France
² Centre d'Analyse et de Mathématique Sociales (CAMS, UMR 8557 CNRS-EHESS), École des Hautes Études en Sciences Sociales, Paris, France

Corresponding author: ^a laetitia.gauvin@lps.ens.fr

Received: 12 May 2009
Revised: 8 June 2009
Published online: 8 July 2009

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.