Abstract
This paper investigates the effects of fluctuations on critical behavior of two-dimensional periodic arrays of coupled Josephson junctions. Both random fluctuations of the external magnetic field and quantum fluctuations are considered. The standard replica method is used to deal with fluctuations of the magnetic field, and it is shown that weak fluctuations are irrelevant whereas strong fluctuations destroy superconductivity. In the case of medium fluctuations, strong dependence on the lattice structure is found: They are irrelevant on a square lattice while they destroy the effect of the magnetic field on a triangular lattice. Quantum fluctuations are treated with use of a variational method. It is shown that they affect the renormalization-group equation in a significant way and lead to a low-temperature reentrant transition into a normal phase. Also shown is that sufficiently strong quantum fluctuations destroy superconductivity at all temperatures. Limitation of this analysis and relevance to experiments are discussed.
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