Percolation with a threshold at zero: A new universality class

Abstract

We propose a new continuum percolation model that has a percolation threshold at zero: The network conducts no matter how small the volume fraction of conductor. The model is in a different universality class from ordinary percolation, despite the fact that it is defined by a potential with only short-range correlations. The conductivity exponent $t_0$ in two dimensions is calculated in terms of static percolation critical exponents, including a nonstandard exponent x. Static critical exponents are also given in general dimensions. The model may provide a useful description of the pore space of some rocks, which appear to have a percolation threshold at or near zero.