Urban segregation with cheap and expensive residences

TL;DR

This study models urban segregation of rich and poor communities using a random-field Ising model on a lattice, demonstrating how residence costs influence community clustering at different temperatures and field strengths.

Contribution

It introduces a simplified Ising model approach to simulate urban segregation, avoiding complex Schelling models and analyzing effects of temperature and random fields on cluster formation.

Findings

Large domains form at low temperature with small random fields.

High temperature prevents the formation of large segregated domains.

Random field strength significantly influences cluster size and growth.

Abstract

In this paper we study urban segregation of two different communities A and B, poor and rich, distributed randomly on finite samples, to check cheap and expensive residences. For this purpose we avoid the complications of the Schelling model which are not necessary and instead we use the Ising model on 500 x 500 square lattice, which give similar results, with random magnetic field at lower and higher temperatures (kT/J = 2.0, 99.0) in finite times equal to 40, 400, 4000 and 40,000. This random-field Ising magnet is a suitable model, where each site of the square lattice carries a magnetic field h which is randomly up (expensive) or down (cheap). The resulting addition to the energy prefers up spins on the expensive and down spins on the cheap sites. Our simulations were carried out using a 50-lines FORTRAN program. We present at a lower temperature (2.0) a time series of pictures, separating growing from non-growing domains. A small random field (h = +- 0.1) allows for large domains, while a large random field (h = +- 0.9) allows only small clusters. At higher temperature (99.0) we could not obtain growing domains.