The dielectric properties of random R-C networks as an explanation of the 'universal' power law dielectric response of solids

Simulations of the AC electrical characteristics of 2D square networks rand omly filled with resistors or capacitors exhibit many features in common wi th experimental dielectric responses of solids. These include the 'universa l' fractional power law dispersions in permittivity and dielectric loss cha racterized by the Cole-Davidson response function. Simulations are presente d of networks containing different proportions of resistors and capacitors which show that the power law frequency response is accounted for well by t he logarithmic mixing rule. Limiting high and low frequency characteristics are found to be controlled by percolation paths of either resistors or cap acitors. It is suggested that the power law response of a solid could be an indication that it is microscopically inhomogenous, containing an effectiv e microscopic random network of conducting and dielectric insulating island s.