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Related Experiment Video

Updated: Jun 23, 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

Ising model on the Apollonian network with node-dependent interactions.

R F S Andrade1, J S Andrade, H J Herrmann

  • 1Instituto de Física, Universidade Federal da Bahia, 40210-210 Salvador, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 28, 2009
PubMed
Summary
This summary is machine-generated.

This study examines an Ising model on Apollonian networks with degree-dependent interactions. Results show critical behavior shifts with interaction strength, indicating no finite-temperature phase transition in the thermodynamic limit.

Related Experiment Videos

Last Updated: Jun 23, 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
  • Condensed matter physics

Background:

  • The Ising model is a fundamental tool for studying magnetism and phase transitions.
  • Scale-free networks exhibit unique properties due to their heterogeneous degree distributions.
  • Apollonian networks are a specific type of fractal network with hierarchical structures.

Purpose of the Study:

  • To investigate the thermodynamical and magnetic properties of an Ising model on Apollonian networks.
  • To analyze the impact of degree-dependent interaction constants on critical behavior.
  • To compare findings with general frameworks for spin models on scale-free networks.

Main Methods:

  • Utilizing the exact geometrical construction of Apollonian networks.
  • Employing a system of discrete maps for precise thermodynamic limit calculations.
  • Analyzing the influence of the exponent 'mu' on interaction constants J(i,j).

Main Results:

  • Critical behavior transitions from T=infinity (mu=0) to T=0 (mu=1) as 'mu' increases.
  • No true critical behavior at a finite temperature is observed in the thermodynamic limit for mu >= 0.
  • Magnetization and magnetic susceptibility exhibit noncritical scaling properties.

Conclusions:

  • The degree-dependent interactions significantly alter the critical phenomena of the Ising model on Apollonian networks.
  • Apollonian networks display distinct magnetic properties compared to simpler network topologies.
  • The study provides insights into spin models on complex, heterogeneous networks.