title: Critical phase of bond percolation on growing networks.
abstract: 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 N ψ and the mean number of clusters with size s per node follows a power function n s ∝ 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.
authors.affiliation: Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, Japan. hasegawa@stat.t.u-tokyo.ac.jp
authors.forename: Takehisa
authors.initials: T
authors.lastname: Hasegawa
authors.forename: Koji
authors.initials: K
authors.lastname: Nemoto