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

Abstract

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.