Monte Carlo simulations of Josephson-junction arrays with positional disorder

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Abstract
We present the results of Monte Carlo simulations of Josephson-junction arrays with positional disorder, in magnetic fields such that the average number of flux quanta per unit cell is an integer. Granato and Kosterlitz have predicted that such systems should exhibit novel behavior, including a disorder-dependent critical field and a reentrant Kosterlitz-Thouless transition. We find that, for magnetic fields above a field approximately equal to the theoretical critical field, the superconducting phases become essentially randomized for all temperatures, rather than becoming aligned as the temperature decreases. Our results show no clear evidence for a reentrant phase transition in our small (16×16) simulated system. These results are consistent with our experiments on proximity-effect arrays with controlled positional disorder. We suggest that the theoretically proposed reentrance is prevented by either finite-size effects or pinning of vortices due to the disorder.