Percolation on Fractal Lattices

Abstract

Numerical evidence of a percolation phase transition on infinitely ramified exact fractals is presented. The percolation transition is studied by a real-space renormalization-group technique on a family of exact fractal lattices with fractal dimensionality $\overline{d}$ between 1 and 2. The critical exponents for percolation depend strongly on the geometry of the fractals.