A transfer matrix study of conductivity and permeability exponents in continuum percolation

The conductivity and permeability exponents for the Swiss cheese model of continuum percolation are calculated numerically, using the transfer matrix method. In two dimensions, the conductivity exponent, t, is shown to equal its universal value t un =1.24, while the permeability exponent e=2.53 is considerably larger. The same exponents in three dimensions are also determined and found to be t=2.46 and e=4.1, greatly exceeding the universal value t un =1.95. The results are in fair agreement with earlier theoretical predictions.