Critical phase of bond percolation on growing networks

概要

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The critical phase of bond percolation on the random growing tree is examined. It is shown that the root cluster grows with the system size N as Nψ and the mean number of clusters with size s per node follows a power function ns ∝ s(-τ) in the whole range of open bond probability p. The exponent τ and the fractal exponent ψ are also derived as a function of p and the degree exponent γ and are found to satisfy the scaling relation τ=1 + ψ^[-1]. Numerical results with several network sizes are quite well fitted by a finite-size scaling for a wide range of p and γ, which gives a clear evidence for the existence of a critical phase.