  In this paper we prove novel lower bounds for the Ginzburg-Landau energy with
or without magnetic field. These bounds rely on an improvement of the "vortex
balls construction" estimates by extracting a new positive term in the energy
lower bounds. This extra term can be conveniently estimated through a Lorentz
space norm, on which it thus provides an upper bound. The Lorentz space
$L^{2,\infty}$ we use is critical with respect to the expected vortex profiles
and can serve to estimate the total number of vortices and get improved
convergence results.
