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In this paper we study urban segregation of two different communities A andB, poor and rich, distributed randomly on finite samples, to check cheap andexpensive residences. For this purpose we avoid the complications of theSchelling model which are not necessary and instead we use the Ising model on500 x 500 square lattice, which give similar results, with random magneticfield at lower and higher temperatures (kT/J = 2.0, 99.0) in finite times equalto 40, 400, 4000 and 40,000. This random-field Ising magnet is a suitablemodel, where each site of the square lattice carries a magnetic field h whichis randomly up (expensive) or down (cheap). The resulting addition to theenergy prefers up spins on the expensive and down spins on the cheap sites. Oursimulations were carried out using a 50-lines FORTRAN program. We present at alower temperature (2.0) a time series of pictures, separating growing fromnon-growing domains. A small random field (h = +- 0.1) allows for largedomains, while a large random field (h = +- 0.9) allows only small clusters. Athigher temperature (99.0) we could not obtain growing domains.

Urban segregation with cheap and expensive residences