Possible destruction of the ordered phase in Josephson-junction arrays with positional disorder

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Abstract
The Josephson-junction array with an integer number of flux quanta per plaquette in the presence of a magnetic field and with geometrical irregularities can be described by the XY model with some random distribution of phase shifts on the bonds (so-called positional disorder). We show that the existing theoretical understanding of the properties of this model is based on an incomplete analysis. The form of the higher-order corrections indicates that the phase with quasi-long-range order, in which the vortices are bound in pairs in the presence of positional disorder, is probably no longer stable. The experimental observation of a superconducting transition in Josephson-junction arrays with small disorder may be then ascribed to finite-size effects.