Critical Behaviour of Conductivity and Dielectric Constant near the Metal‐Non‐Metal Transition Threshold

A system consisting of randomly distributed metallic and dielectric regions is considered. The metal‐non‐metal transition takes place when the volume fraction of the metallic phase approaches the percolation threshold. It is shown that the static dielectric constant diverges near the threshold. Critical indexes are introduced which describe the behaviour of the conductivity and the dielectric constant near the threshold as functions of the volume fraction and frequency. The case of non‐zero dc conductivity of dielectric regions is considered also. It is shown that all indexes describing the critical behaviour of complex conductivity can be expressed by two indexes which are known from computer and model experiments. The results of computer calculations of Webman et al. are analysed.