The analytical properties of the effective static permittivity of a two-component medium

The analytic properties of the dimensionless static effective permittivity f(p, h) of the three-dimensional Rayleigh model as a function of complex variable h are considered. The only singularities of f(p, h) are shown to be first-order poles at real negative h values that form an infinite discrete (denumerable) set. The concentration dependence of the positions of the first four f(p, h) function poles and remainders in them were calculated and presented in the graphic form. An approximate pole-type equation valid over a wide range of concentration p and complex argument h variations was suggested for f(p, h). The results can be used to consistently describe low-frequency dispersion of the effective permittivity of the model under consideration.