Since electrified interfaces are too complex for a fully microscopic approach, in this paper we look for a plausible phenomenological description using methods of statistical field theory. Using simple models for the ideally polarizable interface, the archetype of electrified interfaces, we show that these methods can be fruitfully employed for such a description. The cornerstone of our approach is the introduction of a stochastic field variable with the probability distribution given by an effective Hamiltonian being a functional of the field. The Gibbs energy dependence on charge density can be then obtained using functional integration over the field. For a purely coulombic system our approach leads to the linearized Gouy-Chapman theory. We also study a simple model in which the non-coulombic interaction plays the major role. We build the Hamiltonian step by step to understand the role of the basic ingredients the Gaussian fluctuation and the entropy of mixing. Although the model is crude, it yields a discussion of the gross experimental features of the differential capacity and entropy of formation data in aprotic solvents from a new standpoint.