Finite-size scaling of percolation on scale-free networks

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

Chaos, Solitons & Fractals, 2025, vol. 200, issue P2

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.

Keywords: Finite-size scaling; Percolation; Scale-free network (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:200:y:2025:i:p2:s0960077925010896

DOI: 10.1016/j.chaos.2025.117076

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