The effects of positional disorder on the critical behavior of a two-dimensional Josephson-junction array in a magnetic field are investigated both analytically and numerically. The standard replica method is used to analyze this disordered system, which is a physical realization of the two-dimensional gauge glass. It is shown that in the fully frustrated case, weak positional disorder does not change the critical behavior of the pure system although the critical temperature is lowered. Numerical simulations show that the sharpness of the transition is indeed preserved under weak positional disorder. For sufficiently strong disorder, evidence of the transition disappears from the Monte Carlo simulations. Evidence for or against a reentrant transition at low temperature is inconclusive.

• Received 10 July 1986

DOI:https://doi.org/10.1103/PhysRevB.35.1669