  The critical behavior of frustrated Josephson-junction arrays at $f=1/2$ flux
quantum per plaquette is considered. Results from Monte Carlo simulations and
transfer matrix computations support the identification of the critical
behavior of the square and triangular classical arrays and the one-dimensional
quantum ladder with the universality class of the XY-Ising model. In the
quantum ladder, the transition can happen either as a simultaneous ordering of
the $Z_2$ and $U(1)$ order parameters or in two separate stages, depending on
the ratio between interchain and intrachain Josephson couplings. For the
classical arrays, weak random plaquette disorder acts like a random field and
positional disorder as random bonds on the $Z_2$ variables. Increasing
positional disorder decouples the $Z_2$ and $U(1)$ variables leading to the
same critical behavior as for integer $f$.
