  We consider the two-dimensional one-component plasma without a background and
confined to a half plane near a metal wall. The particles are also subjected to
an external potential acting perpendicular to the wall with an inverse power
law Boltzmann factor. The model has a known solvable isotherm which exhibits a
Kosterlitz-Thouless type transition from a conductive to an insulator phase as
the power law is varied. This allows predictions of theoretical methods of
analysing the Kosterlitz-Thouless transition to be compared with the exact
solution. In particular we calculate the asymptotic density profile by
resumming its low fugacity expansion near the zero-density critical coupling in
the insulator phase, and solving a mean-field equation deduced from the first
BGY equation. Agreement with the exact solution is obtained. As the former
calculation makes essential use of the nested dipole hypothesis of Kosterlitz
and Thouless, the validity of this hypothesis is explicitly verified.
