Coupled electrons and pair fluctuations in two dimensions: a transition to superconductivity in a conserving approximation

We report on a fully self-consistent determination of a phase transition to a superconducting state in a conserving approximation. The transition temperature calculated for a two-dimensional Hubbard model with an attractive interaction in the fluctuation exchange approximation agrees with quantum Monte Carlo calculations. The temperature dependences of the superfluid density and of the specific heat near Tc indicate that the phase transition in this model of coupled collective degrees of freedom and electronic degrees of freedom is consistent with neither mean-field theory, Gaussian fluctuations about a mean field order parameter, nor unbinding Kosterlitz-Thouless vortices.