  We present an analysis of the magnetic response of a mesoscopic
superconductor, i.e. a system of sizes comparable to the coherence length and
to the London penetration depth. Our approach is based on special properties of
the two dimensional Ginzburg-Landau equations, satisfied at the dual point
$(\kappa = \frac{1}{\sqrt{2}}).$ Closed expressions for the free energy and the
magnetization of the superconductor are derived. A perturbative analysis in the
vicinity of the dual point allows us to take into account vortex interactions,
using a new scaling result for the free energy. In order to characterize the
vortex/current interactions, we study vortex configurations that are out of
thermodynamical equilibrium. Our predictions agree with the results of recent
experiments performed on mesoscopic aluminium disks.
