New universality class in percolation on multifractal scale-free planar stochastic lattice

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 percolation threshold $p_c$ and by a set of critical exponents $\beta$, $\gamma$, $\nu$ which describe the critical behavior of percolation probability $P(p)\sim (p_c-p{)}^{\beta }$, mean cluster size $S\sim (p_c-p{)}^{-\gamma }$ and the correlation length $\xi \sim (p_c-p{)}^{-\nu }$. Besides, the exponent $\tau$ characterizes the cluster size distribution function $n_s(p_c)\sim s^{-\tau }$ and the fractal dimension $d_f$ the spanning cluster. We obtain an exact value for $p_c$ and for all these exponents. Our results suggest that the percolation on WPSL belong to a new universality class as its exponents do not share the same value as for all the existing planar lattices.

arXiv comment5 pages, 5 figures

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