Geometrical effects in the conductivity of low dimensional structures

This work is an experimental study on percolation and electrical conductivity in two-dimensions with an aim of confirming some of the theoretical predictions, and measuring some of the parameters introduced in the theory. These parameters include the percolation threshold p , the critical exponents p and t for the percolation probability P(p) and electrical conductivity respectively. We wish to compare the electrical conductivity versus the probability of removed sites (1-p) for the four different common lattice types namely square, triangular, kagome' and honeycomb lattices. In particular, we wish to determine the percolation threshold p for these lattices \*f experimentally and obtain the electrical conductivity critical exponent t within the critical regions of these geometrical lattices. We further wish to show the dependence of the system size length L on the electrical conductivity for the four different lattices mentioned above and obtain the value of t/v, where v is the correlation length critical exponent