Critical behavior of Josephson-junction arrays at f=1/2

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 $f$.