Critical Behavior of the Two-Dimensional Sticks System

Abstract

Percolation critical exponents are derived, for the first time, for a two-dimensional system of randomly distributed conducting sticks, which provides a very convenient model for the study of continuum percolation. In the present computer study it was found that the corresponding conductivity exponent, $t$, has the value of 1.24\ifmmode\pm\else\textpm\fi{}0.03 and that the cluster exponents $\ensuremath{\beta}$, $\ensuremath{\gamma}$, and $\ensuremath{\tau}$ have the values 0.14\ifmmode\pm\else\textpm\fi{}0.02, 2.3\ifmmode\pm\else\textpm\fi{}0.2, and 2.0\ifmmode\pm\else\textpm\fi{}0.1, respectively. These results, which are in excellent agreement with values derived for lattices, show that the conductivities of continuum systems and of lattice systems belong to the same universality class.