Droplet finite-size scaling of the contact process on scale-free networks revisited.
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Date
2023
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Abstract
We present an alternative finite-size scaling (FSS) of the contact process on scale-free networks
compatible with mean-field scaling and test it with extensive Monte Carlo simulations. In our
FSS theory, the dependence on the system size enters the external field, which represents
spontaneous contamination in the context of an epidemic model. In addition, dependence on the
finite size in the scale-free networks also enters the network cutoff. We show that our theory
reproduces the results of other mean-field theories on finite lattices already reported in the
literature. To simulate the dynamics, we impose quasi-stationary states by reactivation. We
insert spontaneously infected individuals, equivalent to a droplet perturbation to the system
scaling as N⁻¹. The system presents an absorbing phase transition where the critical behavior
obeys the mean-field exponents, as we show theoretically and by simulations. However, the
quasi-stationary state gives finite-size logarithmic corrections, predicted by our FSS theory, and
reproduces equivalent results in the literature in the thermodynamic limit. We also report the
critical threshold estimates of basic reproduction number R₀ λc of the model as a linear
function of the network connectivity inverse 1/z, and the extrapolation of the critical threshold function for z→∞ yields the basic reproduction number R₀ = 1 of the complete graph, as
expected. Decreasing the network connectivity increases the critical R₀ for this model.
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Keywords
Barabási-Albert network, Epidemic processes, Directed percolation, Continuous phase transition, Logarithmic corrections
Citation
ALENCAR, D. S. M. et al. Droplet finite-size scaling of the contact process on scale-free networks revisited. International Journal of Modern Physics C, v. 35, artigo 2350105, fev. 2022. Disponível em: <https://www.worldscientific.com/doi/10.1142/S012918312350105X>. Acesso em: 03 maio 2023.