Absence of reentrance in superconducting arrays with positional disorder

A Josephson junction array with geometrical irregularities in the presence of a perpendicular magnetic field can be described by a two-dimensional XY model with random phase shift. If the magnitude of the field corresponds to the integer number of flux quanta per plaquette (on the average), the problem can be discussed in terms of a two-dimensional Coulomb gas interacting with a random potential, the correlations of which diverge logarithmically. In the present work we study the renormalization of the vortex interaction and random potential distribution in such a system and show that its phase diagram cannot include a low-temperature reentrant transition into a disordered phase. Our conclusions are in agreement with the results of both real and computer experiments and can be of relevance for a number of other systems.