MEAN-FIELD THEORIES FOR THE QUANTUM PHASE-TRANSITION IN JOSEPHSON-JUNCTION ARRAYS

We compare two different approaches which both attempt to describe the zero-temperature superconductor-insulator transition in Josephson jun ction arrays through an effective Ginzburg-Landau functional. Both met hods agree only for the special case of a diagonal capacitance matrix (self-charging limit). While the differences in the phase diagram are less significant, we find that the fourth order term of the ''coarse-g rained'' functional changes its sign when the range of the interaction , lambda, exceeds a few lattice constants. On the other hand, a variat ional ansatz predicts a positive sign with a coefficient which increas es with increasing lambda, which implies a large critical region and s trong correlation between order parameter fluctuations.