Percolation and Universality

In this thesis a detailed discussion of the topic percolation theory in squared lattices in two dimensions will be conducted. To support this discussion numerical calculations will be done. For the data analysis and simulations the Hoshen-Kopelman-Algorithm [2] will be used. All concepts deduced will nally lead to the determination of the conductance's exponent t in random resistor networks. Using Derrida's transfer matrix program to calculate the conductivity of random resistors in two and three dimensions [11] and the nite-size scaling approach were used. In two dimensions t= = 0:955 0:006 was obtained. Were is the exponent of the correlation length in innite lattices. This value is in excellent agreement with Derrida ( t= = 0:960:02, [11]) and slightly smaller than Sahimi ( t= = 0:97480:001, [21]). In three dimensions the same approach yielded t= = 2:155 0:012 which some what smaller than the value found by Sahimi t= = 2 :27 0:20 [21] and Gingold and Lobb t= = 2:276 0:012 [25]