COMPARISON OF ISING MAGNET ON DIRECTED VERSUS UNDIRECTED ERD�OS R�ENYI AND SCALE-FREE NETWORKS

Sumour, Muneer A. and EL-ASTAL, Ali H. and Lima, F. W. and Shabat, Mohammed M. and Khalil, H.M. (2007) COMPARISON OF ISING MAGNET ON DIRECTED VERSUS UNDIRECTED ERD�OS R�ENYI AND SCALE-FREE NETWORKS. International Journal of Modern Physics C, 18 (1). pp. 53-60.

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Abstract

Scale-free networks are a recently developed approach to model the interactions found in complex natural and man-made systems. Such networks exhibit a power-law distribution of node link (degree) frequencies n(k) in which a small number of highly connected nodes predominate over a much greater number of sparsely connected ones. In contrast, in an Erd�os{Renyi network each of N sites is connected to every site with a low probability p (of the order of 1=N). Then the number k of neighbors will uctuate according to a Poisson distribution. One can instead assume that each site selects exactly k neighbors among the other sites. Here we compare in both cases the usual network with the directed network, when site A selects site B as a neighbor, and then B in uences A but A does not in uence B. As we change from undirected to directed scale-free networks, the spontaneous magnetization vanishes after an equilibration time following an Arrhenius law, while the directed ER networks have a positive Curie temperature.

Item Type: Article
Uncontrolled Keywords: Ising model; directed and undirected Erd�os{R�enyi network; Barab�asi{Albert network.
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: 01 Apr 2018 10:01
Last Modified: 01 Apr 2018 10:01
URI: http://scholar.alaqsa.edu.ps/id/eprint/491

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