  Within the sine-Gordon formalism of a two-dimensional neutral classical
Coulomb gas, a convergent expansion with non-perturbative nature is performed
to calculate the thermodynamic potential and construct the phase diagram. It is
shown that truncation at the first order yields the Gaussian approximation. The
second- and third-order corrections are analyzed for the case of small fugacity
and are shown that they substantially improve the Gaussian-approximation phase
diagram. In particular, these corrections introduce a new conducting phase and
make the insulator-conductor coexistence phase end at the conducting phase. The
latter result is in agreement with the prediction made by generalized
renormalization-group calculations.
