Expansion in 1/zfor the transition temperature of granular superconductors

An expansion in powers of 1/z is used to study the effect of phase fluctuations on the transition temperature of a granular superconductor, modeled as an array of Josephson junctions. The lowest-order correction to $T_c$/zJ diverges to negative infinity at the grain diameter α=zJ/U=2 and reaches the value -1/2z when α=∞, which corresponds to the classical XY model. The lowest-order correction to the critical grain diameter is also calculated.