  The existence of a discontinuity in the inverse dielectric constant of the
two-dimensional Coulomb gas is demonstrated on purely numerical grounds. This
is done by expanding the free energy in an applied twist and performing a
finite-size scaling analysis of the coefficients of higher-order terms. The
phase transition, driven by unbinding of dipoles, corresponds to the
Kosterlitz-Thouless transition in the 2D XY model. The method developed is also
used for investigating the possibility of a Kosterlitz-Thouless phase
transition in a three-dimensional system of point charges interacting with a
logarithmic pair-potential, a system related to effective theories of
low-dimensional strongly correlated systems. We also contrast the finite-size
scaling of the fluctuations of the dipole moments of the two-dimensional
Coulomb gas and the three-dimensional logarithmic system to those of the
three-dimensional Coulomb gas.
