Superconducting phase transitions in granular systems

We consider a model for granular superconductors consisting of an array of small superconducting particles interacting by Josephson coupling through insulating barriers. We obtain systematically the various critical regions, critical temperature shifts, and crossover regions between zero- and three-dimensional behavior as functions of measurable sample parameters. The qualitative behavior of the system in the various regimes is analyzed and results for the specific heat and fluctuation conductivity in the Gaussian region above $T_c$ are obtained. The possibility of obtaining large critical regions is emphasized. The conditions for observing the phase-locking transition distinct from quasiordering within the grains are found. Theoretical predictions are compared with existing experimental results.