Percolation on a multifractal scale-free planar stochastic lattice and its universality class

We investigate site percolation on a weighted planar stochastic lattice (WPSL), which is a multifractal and whose dual is a scale-free network. Percolation is typically characterized by a threshold value p_c at which a transition occurs and by a set of critical exponents β , γ , ν which describe the critical behavior of the percolation probability P (p ) , mean cluster size S (p ) , and the correlation length ξ . Besides, the exponent τ characterizes the cluster size distribution function n_s(p_c) and the fractal dimension d_f characterizes the spanning cluster. We numerically obtain the value of p_c and of all the exponents. These results suggest that the percolation on WPSL belong to a separate universality class than on all other planar lattices.