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Optimal size of a complex network.

H Hong1, Beom Jun Kim, M Y Choi

  • 1Korea Institute for Advanced Study, Seoul 130-012, Korea. hhong@kias.re.kr

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 6, 2003
PubMed
Summary
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We studied how an Ising system

Area of Science:

  • Statistical physics
  • Complex networks
  • Computational physics

Background:

  • Ising models are fundamental in statistical mechanics.
  • Small-world networks exhibit unique topological properties.
  • Driven systems show complex dynamics under external fields.

Purpose of the Study:

  • Investigate the response behavior of an Ising system on a small-world network.
  • Analyze the impact of system size on magnetization response.
  • Understand the role of temperature and network structure.

Main Methods:

  • Monte Carlo dynamic simulations were employed.
  • The system was subjected to an oscillating driving field.
  • Rewiring probability and system size were varied.

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Main Results:

  • Occupancy ratio (spin following) shows monotonic behavior at low/high temperatures.
  • A resonance-like peak in occupancy ratio observed at intermediate temperatures.
  • Saturation of occupancy ratio occurs at large system sizes, dependent on temperature.

Conclusions:

  • System size significantly influences the dynamic response of driven Ising systems.
  • Resonant behavior emerges at intermediate temperatures, highlighting complex size-dependent effects.
  • Temperature-dependent saturation indicates a link between system size, correlation length, and network dynamics.