Fluctuations in granular superconductors

By expanding the order parameter for an array of Josephson-coupled grains in powers of 1/z, where z is the number of nearest neighbors, I systematically incorporate the effect of phase fluctuations. The correction of order 1/z vanishes when the mean-field solution is known to be exact, for α=zJ/U=∞ and $T^{\mathrm{*}}$=T/zJ=0. For larger $T^{\mathrm{*}}$ and smaller α, the first-order correction increases until it diverges at the mean-field transition temperature.