  We investigate quantum phase transitions in two-dimensional superconducting
arrays with general capacitance matrices and discrete charge states. We use the
perturbation theory together with the simulated annealing method to obtain the
zero-temperature phase diagrams, which display various lobe-like structures of
insulating solid phases, and examine the possibility of supersolid phase. At
nonzero temperatures, an effective classical Hamiltonian is obtained through
the use of the variational method in the path-integral formalism, and the
corresponding phase diagram is found approximately. The insulating lobes of the
solid phases are shown to exist at sufficiently low temperatures, and results
of Monte Carlo simulations are also presented.
