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We present results from an extensive analytic and numerical study of atwo-dimensional model of a square array of ultrasmall Josephson junctions. Weinclude the ultrasmall self and mutual capacitances of the junctions, for thesame parameter ranges as those produced in the experiments. The modelHamiltonian studied includes the Josephson, $E_J$, as well as the charging,$E_C$, energies between superconducting islands. The corresponding quantumpartition function is expressed in different calculationally convenient wayswithin its path-integral representation. The phase diagram is analyticallystudied using a WKB renormalization group (WKB-RG) plus a self-consistentharmonic approximation (SCHA) analysis, together with non-perturbative quantumMonte Carlo simulations. Most of the results presented here pertain to thesuperconductor to normal (S-N) region, although some results for the insulatingto normal (I-N) region are also included. We find very good agreement betweenthe WKB-RG and QMC results when compared to the experimental data. To fit thedata, we only used the experimentally determined capacitances as fittingparameters. The WKB-RG analysis in the S-N region predicts a low temperatureinstability i.e. a Quantum Induced Transition (QUIT). We carefully simulationsand carry out a finite size analysis of $T_{QUIT}$ as a function of themagnitude of imaginary time axis $L_\tau$. We find that for some relativelylarge values of $\alpha=E_C/E_J$ ($1\leq \alpha \leq 2.25)$, the$L_\tau\to\infty$ limit does appear to give a {\it non-zero} $T_{QUIT}$, whilefor $\alpha \ge 2.5$, $T_{QUIT}=0$. We use the SCHA to analytically understandthe $L_\tau$ dependence of the QMC results with good agreement between them.Finally, we also carried out a WKB-RG analysis in the I-N region and found noevidence of a low temperature QUIT, up to lowest order in ${\alpha}^{-1}$Comment: 39 pages, 18 postscript figures, to appear in Phys. Rev.

Critical properties of two-dimensional Josephson-junction arrays with zero-point quantum fluctuations