  Using numerical simulations, a vortex is studied in the broken phase of the
$(2+1)$-d $O(2)$-symmetric scalar field theory in the vicinity of the
Wilson-Fisher fixed point. The vortex is an infraparticle that is surrounded by
a cloud of Goldstone bosons. The $L$-dependence of the vortex mass in a finite
$C$-periodic volume $L^2$ leads to the determination of the renormalized vortex
charge.
