The order of the metal to superconductor transition

We present results from large-scale Monte Carlo simulations on the full Ginzburg-Landau (GL) model, including fluctuations in the amplitude and the phase of the matter-field, as well as fluctuations of the non-compact gauge-field of the theory. {}From this we obtain a precise critical value of the GL parameter $\text{kct}$ separating a first order metal to superconductor transition from a second order one, $\text{kct}=(0.76\pm 0.04)\mathrm{/}\sqrt{2}$. This agrees surprisingly well with earlier analytical results based on a disorder theory of the superconductor to metal transition, where the value $\text{kct}=0.798\mathrm{/}\sqrt{2}$ was obtained. To achieve this, we have done careful infinite volume and continuum limit extrapolations. In addition we offer a novel interpretation of $\text{kct}$, namely that it is also the value separating \typeI and \typeII behaviour.<