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Related Experiment Videos

Correlations in interacting systems with a network topology.

S N Dorogovtsev1, A V Goltsev, J F F Mendes

  • 1Departamento de Física da Universidade de Aveiro, 3810-193 Aveiro, Portugal. sdorogov@fis.ua.pt

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 21, 2006
PubMed
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Pair correlations in complex networks decay rapidly with distance. On networks with fat-tailed distributions, only nearest-neighbor interactions are observable, weakening distant correlations.

Area of Science:

  • Statistical physics
  • Network science
  • Complex systems

Background:

  • Interacting systems on networks exhibit complex correlation behaviors.
  • Understanding these correlations is crucial for various scientific domains.

Purpose of the Study:

  • To investigate the decay of pair correlations in interacting systems on complex networks.
  • To analyze the impact of network topology, specifically fat-tailed degree distributions, on correlation strength.

Main Methods:

  • Analytical study of pair correlations as a function of distance (l).
  • Calculation of the mean number of lth nearest neighbors (zl).
  • Exact derivation of the pair correlation function for the Ising model on complex networks.

Main Results:

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  • Pair correlations generally decay faster than 1/(lzl).
  • Fat-tailed degree distributions lead to a dramatic weakening of correlations beyond nearest neighbors.
  • Only nearest-neighbor correlations are observable in large networks with divergent z2.

Conclusions:

  • The structure of complex networks significantly influences correlation decay.
  • The findings provide a precise understanding of correlation behavior in systems like the Ising model on diverse network topologies.