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.
|Journal||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics|
|Publication status||Published - 2010 May 7|
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics