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Finite-size scaling of percolation on scale-free networks

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  • Zhao, Xuewei
  • Yang, Liwenying
  • Peng, Dan
  • Liu, Run-Ran
  • Li, Ming

Abstract

Critical phenomena on scale-free networks with a degree distribution pk∼k−λ exhibit rich finite-size effects due to its structural heterogeneity. We systematically study the finite-size scaling of percolation and identify two distinct crossover routes to mean-field behavior: one controlled by the degree exponent λ, the other by the degree cutoff K∼Vκ, where V is the system size and κ∈[0,1] is the cutoff exponent. Increasing λ or decreasing κ suppresses heterogeneity and drives the system toward mean-field behavior, with logarithmic corrections near the marginal case. These findings provide a unified picture of the crossover from heterogeneous to homogeneous criticality. In the crossover regime, we observe rich finite-size phenomena, including the transition from vanishing to divergent susceptibility, distinct exponents for the shift and fluctuation of pseudocritical points, and a numerical clarification of previous theoretical predictions.

Suggested Citation

  • Zhao, Xuewei & Yang, Liwenying & Peng, Dan & Liu, Run-Ran & Li, Ming, 2025. "Finite-size scaling of percolation on scale-free networks," Chaos, Solitons & Fractals, Elsevier, vol. 200(P2).
    • Handle: RePEc:eee:chsofr:v:200:y:2025:i:p2:s0960077925010896
    DOI: 10.1016/j.chaos.2025.117076
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    References listed on IDEAS

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    1. Manna, S.S. & Chatterjee, Arnab, 2011. "A new route to Explosive Percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(2), pages 177-182.
    2. Filippo Radicchi & Claudio Castellano, 2015. "Breaking of the site-bond percolation universality in networks," Nature Communications, Nature, vol. 6(1), pages 1-7, December.
    3. J.-S. Lee & K.-I. Goh & B. Kahng & D. Kim, 2006. "Intrinsic degree-correlations in the static model of scale-free networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 49(2), pages 231-238, January.
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