Year: 2025
Type: article
Abstract: We investigate bond percolation on the Song–Havlin–Makse (SHM) network, a scale-free tree with a tunable degree exponent and dimensionality. Using a generating function approach, we analytically derive the average size and the fractal exponent of the root cluster for deterministic cases. Our analysis reveals that bond percolation on the SHM network remains in a non-percolating phase for all p < 1 when the network is fractal (i.e. finite-dimensional), whereas it exhibits a critical phase, where the cluster size distribution follows a power-law with a p-dependent exponent, throughout the entire range of p when the network is small-world (i.e. infinite-dimensional), regardless of the specific dimensionality or degree exponent. The analytical results are in excellent agreement with Monte Carlo simulations.
Authors: Kazuki Wataya, Takehisa Hasegawa
Institution: Ibaraki University
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414916674