Measurement of the conductivity exponent in two-dimensional percolating networks: square lattice versus random-void continuum.

Abstract

Using an analog simulation technique, we have studied the conductivity transition in two-dimensional percolating networks. A computer-controlled x-y plotter scribes a percolating pattern on a sheet of aluminized plastic while the resistance of the sheet is continuously monitored. With this technique, we have measured the conductivity exponent t for two systems: site percolation on a square lattice and random-void continuum percolation. We find t=1.29\ifmmode\pm\else\textpm\fi{}0.03 for the lattice and t=1.34\ifmmode\pm\else\textpm\fi{}0.07 for the continuum, in agreement with a recent theoretical prediction that the conductivity exponents for these two systems are the same. We have also verified a theoretical estimate of the magnitude of conductance fluctuations due to finite-size effects.