ABSTRACT

Field-theoretic functional integral methods can be used to study

exact solutions of models on the basis of a one-dimensional (1D)

Coulomb gas with charged boundaries. In 1D, exactly solvable

Coulomb gas models can be then used as a testbed for assessing the

accuracy of various approximations: the weak coupling expansion,

Poisson-Boltzmann (PB)/mean-field (MF) equations, and the strong

coupling expansion [1]. We review these approximations in the

context of three 1D Coulomb gas systems and remark on whether

or not they fail to predict important effects present in the exact

solution.