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