Highly Nonlinear Ising Model and Social Segregation

Sumour, Muneer A. and Radwan, Mohammed A. and Shabat, Mohammed M. (2012) Highly Nonlinear Ising Model and Social Segregation. IUG Journal of Natural and Engineering Studies, 20 (2). pp. 15-28. ISSN 1726-6807

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Abstract

The usual interaction energy of the random field Ising model in statistical physics is modified by complementing the random field by adding to the energy of the usual Ising model a nonlinear term S n , where S is the sum of the neighbor spins, and n=0,1,3,5,7,9,11. Within the Schelling model of urban segregation, this modification corresponds to housing prices depending on the immediate neighborhood. Simulations at different temperatures (T), lattice size (L), magnetic field (h), number of neighbors (m) and different time intervals (number of iterations) showed that results for all n are similar, expect for n=3 in violation of the universality principle and the law of corresponding states. In order to find the critical temperatures, for large n we no longer start with all spins parallel but instead with a random configuration, in order to facilitate spin flips. However, in all cases we have a Curie temperature with phase separation or long-range segregation only below this Curie temperature, and it is approximated by a simple formula: Tc is proportional to m*exp(n/constant)

Item Type: Article
Subjects: Q Science > QC Physics
Divisions: Faculty of Engineering, Science and Mathematics > School of Physics
Depositing User: د. منير احمد عبد القادر سمور
Date Deposited: 02 Apr 2018 07:41
Last Modified: 02 Apr 2018 07:41
URI: http://scholar.alaqsa.edu.ps/id/eprint/583

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