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 kappa(tri) separating a first-order metal-to-superconductor transition from a second-order one, kappa(tri) = (0.76+/-0.04)/root2. This agrees surprisingly well with earlier analytical results based on a disorder theory of the superconductor to metal transition, where the value kappa(tri) = 0.798/root2 was obtained. To achieve this, we have done careful infinite volume and continuum limit extrapolations. In addition we offer an interpretation of kappa(tri), namely, that it is also the value separating type-I and type-II behavior.