Statistical physics of the Schelling model of segregation

Abstract

This paper explores the 1D Schelling model’s statistical physics, focusing on segregation and unhappiness coefficients across varied vacancy densities and magnetization values. Derived from the interdisciplinary field of Sociophysics, the 1D variant offers computational efficiency. The study reveals increasing segregation with rising vacancy density, emphasizing potential second-order transitions. Unhappiness decreases with more vacancies, displaying abrupt yet continuous shifts, suggesting potential phase transitions. Finite-size effects underscore the need for larger grid simulations. These findings provide a foundation for deeper investigations into Schelling model dynamics and phase transitions in diverse scenarios