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Ising model in clustered scale-free networks.

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  • 1Instituto de Ciencia de Materiales, Consejo Superior de Investigaciones Científicas (CSIC), Campus de Cantoblanco, 28049 Madrid, Spain.

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This summary is machine-generated.

Clustering in scale-free networks affects the Ising model

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Area of Science:

  • Statistical physics
  • Network science
  • Complex systems

Background:

  • Scale-free networks exhibit a power-law degree distribution P(k) ~ k^(-γ).
  • Clustering, or the presence of triangles, introduces local structure into networks.
  • The Ising model is a fundamental model for studying magnetic phase transitions.

Purpose of the Study:

  • Investigate the impact of clustering on the ferromagnetic-paramagnetic phase transition of the Ising model in scale-free networks.
  • Analyze how network properties, specifically the degree distribution exponent (γ) and triangle density, influence transition temperatures.
  • Determine the role of clustering in promoting ferromagnetic correlations.

Main Methods:

  • Monte Carlo simulations were employed to study the Ising model.
  • Scale-free networks with varying degree distribution exponents (γ) and triangle densities were generated.
  • The behavior of the system was analyzed in the thermodynamic limit (N→∞) and for finite system sizes.

Main Results:

  • For γ > 3, a distinct phase transition occurs at T(c)(γ), which increases with triangle density due to changes in mean connectivity.
  • For γ ≤ 3, a crossover from ferromagnetic to paramagnetic behavior occurs at T(co), which is size-dependent and increases with clustering.
  • For γ ≤ 3, clustering enhances ferromagnetic correlations, raising the crossover temperature even for networks with identical degree distributions.

Conclusions:

  • Clustering significantly influences the magnetic properties of the Ising model on scale-free networks.
  • The presence of triangles can stabilize ferromagnetic order, particularly in networks with lower degree exponents (γ ≤ 3).
  • Network topology, specifically clustering, plays a crucial role in determining phase transition or crossover behavior.