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Related Experiment Video

Updated: May 16, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

Nonequilibrium model on Apollonian networks.

F W S Lima1, André A Moreira, Ascânio D Araújo

  • 1Dietrich Stauffer Computational Physics Lab, Departamento de Física, Universidade Federal do Piauí, 64049-550, Teresina - PI, Brazil. fwslima@gmail.com

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 11, 2012
PubMed
Summary
This summary is machine-generated.

The majority-vote model exhibits a phase transition on Apollonian networks, unlike the Ising model. Rewiring network links alters critical behavior, indicating a distinct universality class.

Related Experiment Videos

Last Updated: May 16, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

Area of Science:

  • Statistical mechanics
  • Complex networks
  • Phase transitions

Background:

  • Apollonian networks are fractal structures with unique topological properties.
  • The majority-vote model is a fundamental tool for studying social and physical phenomena.
  • Previous studies on equilibrium models like the Ising model on Apollonian networks found no phase transition.

Purpose of the Study:

  • To investigate the presence of a phase transition in the majority-vote model on Apollonian networks.
  • To analyze the impact of network structure modifications (link rewiring) on the model's behavior.
  • To determine if the majority-vote model shares the same universality class as the Ising model on these networks.

Main Methods:

  • Monte Carlo simulations were employed to study the majority-vote model.
  • The effects of varying the noise parameter (q) and link rewiring probability (p) were systematically analyzed.
  • Critical exponents and critical noise values were calculated to characterize the phase transition.

Main Results:

  • The majority-vote model demonstrates a clear phase transition as a function of the noise parameter q on Apollonian networks.
  • Link rewiring significantly influences the critical behavior, affecting calculated exponent ratios (γ/ν, β/ν, 1/ν).
  • The critical noise (qc) and the critical noise U were determined for different rewiring probabilities.

Conclusions:

  • The majority-vote model exhibits distinct critical phenomena on Apollonian networks compared to equilibrium models.
  • The findings suggest that the majority-vote model on Apollonian networks belongs to a different universality class than the equilibrium Ising model.
  • Network topology and dynamics interact to produce diverse phase transition behaviors in complex systems.