  We consider the effect of positional disorder on a Josephson junction array
with an applied magnetic field of f=1/2 flux quantum per unit cell. This is
equivalent to the problem of random Gaussian phase shifts in the fully
frustrated 2D XY model. Using simple analytical arguments and numerical
simulations, we present evidence that the ground state vortex lattice of the
pure model becomes disordered, in the thermodynamic limit, by any amount of
positional disorder.
