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Phase Transition In The Ising Model On Local-World Evolving Networks

Author

Listed:
  • WEI QIANG

    (School of Computer, China University of Geosciences, Wuhan 430074, People's Republic of China;
    Faculty of Earth Resources, China University of Geosciences, Wuhan 430074, People's Republic of China)

  • GUANGDAO HU

    (Faculty of Earth Resources, China University of Geosciences, Wuhan 430074, People's Republic of China)

  • PENGDA ZHAO

    (Faculty of Earth Resources, China University of Geosciences, Wuhan 430074, People's Republic of China)

Abstract

We study the critical behavior of the Ising model on the local-world evolving network. Monte Carlo simulations with the standard Metropolis local update algorithms are performed extensively on the network with different parameters. Ising spins put onto network vertices exhibit an effective phase transition from ferromagnetism to paramagnetism upon heating. The critical temperature has been demonstrated to increase linearly with the average degree of the network asTC~ 〈k〉. Simulation results on local-world evolving networks with various parameters show logarithmical relationships of the critical temperature with the size of the local world asTC~ln(ml), and with the size of the network asTC~ln(N), respectively. The latter is the generalization of the conclusion for the Ising model on the Barabási–Albert scale-free network, a limiting case of the local-world evolving network.

Suggested Citation

  • Wei Qiang & Guangdao Hu & Pengda Zhao, 2008. "Phase Transition In The Ising Model On Local-World Evolving Networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 19(11), pages 1717-1726.
    • Handle: RePEc:wsi:ijmpcx:v:19:y:2008:i:11:n:s0129183108013242
    DOI: 10.1142/S0129183108013242
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