On the Nature of the Phase Transition Triggered by Vortex-Like Deffects in the 2D Ginzburg-Landau Model

The two dimensional lattice Ginzburg-Landau hamiltonian is simulated numerically for different values of the coherence length $\xi$ in units of the lattice spacing $a$, a parameter which controls amplitude fluctuations. The phase diagram on the plane $T-\xi$ is measured. Amplitude fluctuations change dramatically the nature of the phase transition: for values of $\xi/a \simeq 1$, instead of the smooth Kosterlitz-Thouless transition there is a {\em first order} transition with a discontinuity in the vortex density $v$ and a sharper drop in the helicity modulus $\mathrm{\Gamma }$. Both observables $v$ and $\mathrm{\Gamma }$ are analyzed in detail at the crossover region between first and second order which occurs for intermediate values of $\xi \mathrm{/}a$.