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XY model in small-world networks.

B J Kim1, H Hong, P Holme

  • 1Department of Theoretical Physics, Umeå University, 901 87 Umeå, Sweden.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 12, 2001
PubMed
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Monte Carlo simulations reveal that the XY model on 1D small-world networks exhibits long-range order at finite temperatures, even with minimal rewiring. This suggests a phase transition occurs for any rewiring probability greater than zero.

Area of Science:

  • Statistical Physics
  • Complex Networks
  • Condensed Matter Physics

Background:

  • The XY model is a fundamental model in statistical physics used to study phase transitions.
  • Small-world networks possess unique topological properties, bridging regular and random networks.

Purpose of the Study:

  • To investigate the phase transition behavior of the XY model on one-dimensional small-world networks.
  • To determine the influence of rewiring probability on the system's order and transition temperature.

Main Methods:

  • Monte Carlo simulations were employed to model the XY model on 1D small-world networks.
  • The effects of varying rewiring probabilities were systematically analyzed.

Main Results:

Related Experiment Videos

  • Long-range order was observed at finite temperatures, even for very small rewiring probabilities.
  • The results suggest a finite-temperature phase transition exists for any non-zero rewiring probability.
  • The nature of the phase transition was compared to that of the globally coupled XY model.

    • Conclusions:

    • Small-world network topology significantly impacts the phase transition characteristics of the XY model.
    • The presence of even minimal long-range connections can induce or sustain order at finite temperatures.