COMPARISON OF ISING MAGNET ON DIRECTED VERSUS UNDIRECTED ERDÖS–RÉNYI AND SCALE-FREE NETWORKS

M. A. Sumour (), A. H. El-Astal, F. W. S. Lima (), M. M. Shabat and H. M. Khalil
Additional contact information
M. A. Sumour: Physics Department, Al-Aqsa University, P. O. Box 4051, Gaza, Gaza Strip, Palestinian Authority
A. H. El-Astal: Physics Department, Al-Aqsa University, P. O. Box 4051, Gaza, Gaza Strip, Palestinian Authority
F. W. S. Lima: Departamento de Física, Universidade Federal do Piauí, 64002-150, Teresina - PI, Brazil
M. M. Shabat: Physics Department, Islamic University, P. O. Box 108, Gaza, Gaza Strip, Palestinian Authority;
H. M. Khalil: Physics Department, Ain Shams University, Cairo, Egypt

International Journal of Modern Physics C (IJMPC), 2007, vol. 18, issue 01, 53-60

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) frequenciesn(k)in which a small number of highly connected nodes predominate over a much greater number of sparsely connected ones. In contrast, in an Erdös–Renyi network each ofNsites is connected to every site with a low probabilityp(of the order of1/N). Then the numberkof neighbors will fluctuate according to a Poisson distribution. One can instead assume that each site selects exactlykneighbors 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 influences A but A does not influence 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.

Keywords: Ising model; directed and undirected Erdös–Rényi network; Barabási–Albert network (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1142/S0129183107010346

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