Abstract
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 \ensuremath{\alpha}=zJ/U=\ensuremath{\infty} and ${T}^{\mathrm{*}}$=T/zJ=0. For larger ${T}^{\mathrm{*}}$ and smaller \ensuremath{\alpha}, the first-order correction increases until it diverges at the mean-field transition temperature.
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