The Kramers–Kronig Relations for Permittivity, “True” Screening Radius, and Critical Point of a Coulomb System

A correlation between the peculiarities of the electric permittivity (EP) $\epsilon(q, \omega)$ of a homogenous and isotropic Coulomb system (CS) in the limit of $\omega \to 0$, $q \to 0$ and $q \to 0$, $\omega \to 0$ is established on the basis of exact limiting relations; general expression for static EP $\epsilon(q, 0)$ of a CS is obtained in the region of small wave vectors $q$. The concepts of a “true” dielectric and “ideal” conductor are introduced. The definition of a “true” screening radius is considered. A critical point of two-component CS is shown to correspond to either the “true” dielectric state or the “ideal” conductor one.