THE PHASE-DIAGRAM OF A 2-DIMENSIONAL ARRAY OF MESOSCOPIC GRANULES

A lattice boson model is used to study ordering phenomena in regular 2 D arrays of superconductive mesoscopic granules, Josephson junctions a nd pores filled with superfluid helium. The phase diagram of the syste m, for when quantum fluctuations of both the phase and the local super fluid density are essential, is analysed both analytically and by the quantum Monte Carlo technique. For the system of strongly interacting bosons it is found that as the boson density n(0) is increased the bou ndary of the ordered superconducting state shifts to lower temperature s and at n(0) > 8 approaches its limiting position corresponding to ne gligible relative fluctuations of the moduli of the order parameter (a s in an array of 'macroscopic' granules). In the region of weak quantu m fluctuations of phases, mesoscopic phenomena manifest themselves up to n(0) similar to 10. The mean-field theory and functional integral ( 1/n(0))-expansion results are shown to agree with those of quantum Mon te Carlo calculations of the boson Hubbard model and its quasiclassica l limit, the quantum XY-model.