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http://hdl.handle.net/20.500.12358/24052
TitleHighly Nonlinear Ising Model and Social Segregation
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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 , 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) Keywords: Ising Model, Modified Ising model, Statistical Physics, and Urban Segregation.

Authors
Shabat, Mohammed M.
Radwan, M. A.
Sumour, M. A.
TypeJournal Article
Date2012
LanguageEnglish
Published inIUG Journal for Natural Studies
SeriesVolume: 20, Number: 2
Publisherالجامعة الإسلامية - غزة
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  • Staff Publications- Faculty of Science [1030]
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The institutional repository of the Islamic University of Gaza was established as part of the ROMOR project that has been co-funded with support from the European Commission under the ERASMUS + European programme. This publication reflects the views only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein.

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The institutional repository of the Islamic University of Gaza was established as part of the ROMOR project that has been co-funded with support from the European Commission under the ERASMUS + European programme. This publication reflects the views only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein.

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