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Comparison Of Ising Magnet On Directed Versus Undirected Erdös–Rényi And Scale-Free Networks

Author

Listed:
  • 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;
    Presently at Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strase 38, 01187 Dresden, Germany)

  • H. M. KHALIL

    (Physics Department, Ain Shams University, Cairo, Egypt)

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.

Suggested Citation

  • M. A. Sumour & A. H. El-Astal & F. W. S. Lima & M. M. Shabat & H. M. Khalil, 2007. "Comparison Of Ising Magnet On Directed Versus Undirected Erdös–Rényi And Scale-Free Networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 53-60.
    • Handle: RePEc:wsi:ijmpcx:v:18:y:2007:i:01:n:s0129183107010346
    DOI: 10.1142/S0129183107010346
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    1. ., 2006. "Physical and Social Indicators," Chapters, in: Middle East Oil Exporters, chapter 5, Edward Elgar Publishing.
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