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

TL;DR

This paper provides evidence that in two-dimensional Ginzburg-Landau models, a first order phase transition occurs when the coherence length approaches the lattice spacing, linked to vortex proliferation.

Contribution

It clarifies the conditions under which a first order transition occurs in 2D Ginzburg-Landau models and relates vortex behavior to this transition, contrasting with previous parametrizations.

Findings

First order transition occurs at coherence length comparable to lattice spacing.

Transition linked to sudden vortex proliferation.

Results align with previous studies despite different parametrizations.

Abstract

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.