Comment on "First Order Transition in the Ginzburg-Landau Model"

I present clear evidences that for $d$=2 a first order transition takes place when the coherence length $\xi$ becomes of the order of the lattice spacing and that this is connected with a sudden proliferation of vortices. Similar results where reported in cond-mat/0010119 although using a different parametrization of the G-L model which obscures the comparison with recent results obtained by means of a variational approximation.