A vortex description of the first-order phase transition in type-I superconductors

Using both analytical arguments and detailed numerical evidence we show that the first order transition in the type-I 2D Abelian Higgs model can be understood in terms of the statistical mechanics of vortices, which behave in this regime as an ensemble of attractive particles. The well-known instabilities of such ensembles are shown to be connected to the process of phase nucleation. By characterizing the equation of state for the vortex ensemble we show that the temperature for the onset of a clustering instability is in qualitative agreement with the critical temperature. Below this point the vortex ensemble collapses to a single cluster, which is a non-extensive phase, and disappears in the absence of net topological charge. The vortex description provides a detailed mechanism for the first order transition, which applies at arbitrarily weak type-I and is gauge invariant unlike the usual field-theoretic considerations, which rely on asymptotically large gauge coupling.