  A new approach to the Berezinskii-Kosterlitz-Thouless transition in the
two-dimensional Coulomb gas model is explored by MC simulation and finite size
scaling. The usual mapping of a neutral two-dimensional superconductor in zero
magnetic field to a Coulomb gas leads to an unscreened logarithmic interaction
between the vortices, and with periodic boundary conditions vortex
configurations are always vorticity neutral with an equal number of plus and
minus vortices. We demonstrate that relaxing the neutrality condition has
certain advantages. It leads to non-neutral vortex configurations that can
appear in real systems with open boundary conditions and permits calculation of
the compressibility, which for thin film superconductors corresponds to the
magnetic permeability. The vortex-number fluctuation has remarkable scaling
properties at and below the Berezinskii-Kosterlitz-Thouless transition. The
fugacity variable becomes dangerously irrelevant in the low-temperature phase
and leads to a multiplicative scaling correction to the mean-square
vortex-number fluctuation and to the magnetic permeability. This multiplicative
correction strongly affects the scaling properties of the vorticity fluctuation
at and below the transition. Consequences of these findings are demonstrated
using Monte Carlo simulations. Inclusion of the next-higher order correction to
scaling is found to play an important role in the analysis of numerical data
for the vortex number fluctuation and permits accurate determination of the
critical properties.
