Effect of dissipation on the phase transition in granular superconductors

The phase diagram of the self-charging model of an array of resistively shunted junctions is calculated in the mean-field approximation using the functional integral formulation. The dissipation tends to diminish the effects of the charging energy $U$ on the phase boundary: The degree of reentrance decreases and the boundary approaches the classical $U=0\mathrm{}$ limit as $g\to \infty$.