Bond percolation on the small-world (infinite-dimensional) SHM tree stays in a critical phase for all p < 1 with exact exponent ψ(p) = ln(1+m+mp)/ln(1+2m), while on the fractal (finite-dimensional) SHM tree it stays nonpercolating for all p < 1 with constant ψ = ln m/ln(2m+1).
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Critical and Nonpercolating Phases in Bond Percolation on the Song-Havlin-Makse Network
Bond percolation on the small-world (infinite-dimensional) SHM tree stays in a critical phase for all p < 1 with exact exponent ψ(p) = ln(1+m+mp)/ln(1+2m), while on the fractal (finite-dimensional) SHM tree it stays nonpercolating for all p < 1 with constant ψ = ln m/ln(2m+1).