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Related Experiment Videos

Small-world effects in the majority-vote model.

Paulo R A Campos1, Viviane M de Oliveira, F G Brady Moreira

  • 1Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970 São Carlos, SP, Brazil. prac@caltech.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 15, 2003
PubMed
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We studied the majority-vote model on small-world networks. Rewiring the lattice preserves the phase transition but shifts the critical point and changes the universality class.

Area of Science:

  • Statistical Physics
  • Complex Networks
  • Computational Physics

Background:

  • The majority-vote model is a fundamental tool for studying phase transitions in statistical physics.
  • Small-world networks, characterized by short average path lengths and high clustering, exhibit unique emergent properties.
  • Understanding how network topology influences critical phenomena is crucial for various scientific disciplines.

Purpose of the Study:

  • To investigate the impact of small-world network topology on the majority-vote model.
  • To determine if long-range interactions introduced by rewiring affect the phase transition behavior.
  • To analyze the changes in critical point and universality class due to small-world rewiring.

Main Methods:

  • Rewiring a two-dimensional square lattice to create small-world network structures.

Related Experiment Videos

  • Simulating the majority-vote model on these modified lattices.
  • Analyzing the phase transition behavior and critical phenomena by varying rewiring probability.

    • Main Results:

    • The introduction of long-range interactions via rewiring does not eliminate the critical nature of the majority-vote model.
    • A well-defined phase transition persists even with the modified network topology.
    • The critical point of the model is found to be a monotonically increasing function of the rewiring probability.
    • Small-world effects were observed to alter the universality class of the majority-vote model.

    Conclusions:

    • Small-world networks preserve the critical behavior of the majority-vote model, indicating robustness of the phase transition.
    • Network rewiring significantly influences the critical point and universality class, highlighting the importance of topology.
    • These findings contribute to a deeper understanding of phase transitions in complex systems and network science.