Phase transitions driven by vortices in two-dimensional superfluids and superconductors: From Kosterlitz-Thouless to first order

Amplitude fluctuations can dramatically change the nature of the phase transition in two-dimensional superfluids and superconductors. For sufficiently small values of the quartic term of the Landau-Ginzburg-Wilson, which correspond to coherence lengths comparable with the lattice size, instead of the subtle and smooth topological Kosterlitz-Thouless transition there is a first order transition from a plasma of vortices to a state without vortices, with a sharp jump in the vortex density and a larger nonuniversal drop in the helicity modulus.