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.