Phase Transitions Driven by Vortices in 2D Superfluids and Superconductors: From Kosterlitz-Thouless to 1st Order

The Landau-Ginzburg-Wilson hamiltonian is studied for different values of the parameter $lambda$ which multiplies the quartic term (it turns out that this is equivalent to consider different values of the coherence length $xi$ in units of the lattice spacing $a$). It is observed that amplitude fluctuations can change dramatically the nature of the phase transition: for small values of $lambda$ ($xi/a > 0.7$), instead of the smooth Kosterlitz-Thouless transition there is a {em first order} transition with a discontinuous jump in the vortex density $v$ and a larger non-universal drop in the helicity modulus. In particular, for $lambda$ sufficiently small ($xi/a cong 1$), the density of bound pairs of vortex-antivortex below $T_c$ is so low that, $v$ drops to zero almost for all temperature $T<Tc$.