NonperturbativeXY-model approach to strong coupling superconductivity in two and three dimensions

For an electron gas with δ-function attraction, we investigate the crossover from weak- to strong-coupling superconductivity in two and three dimensions. From mean-field theory we extract the stiffness of phase fluctuations and set up effective XY models which serve to determine nonperturbatively the temperature of phase decoherence where superconductivity breaks down. We find the transition temperature Tc as a monotonous function of the coupling strength both in two and three dimensions, and give analytic formulas for the merging of temperature of phase decoherence with the temperature of pair formation in the weak-coupling limit.