The Bergman spectrum of the effective dielectric constant in two-dimensional composite media

The Bergman spectrum of a two-dimensional composite with parallel cylinders immersed in the matrix was calculated and analysed. We found that the spectrum is discrete away from the percolation threshold and tends towards being continuous as the cylinders become closer and finally touch. We also calculated the effective dielectric constant and found that close to the percolation threshold the effective dielectric constant is scaled with an exponent that is half of the distance between nearest cylinder surfaces, and this was explained by a simple physical argument.