Phase transitions in coupled XY-Ising systems

We study the critical behavior of fully frustrated XY and Josephson-junction systems by means of a coupled XY-Ising model. From Monte Carlo and transfer-matrix calculations, we find separate XY and Ising and first-order transitions, depending on the parameters. In addition, a line of continuous transitions is found, with simulataneous loss of XY and Ising order and novel critical behavior. This result is supported by Monte Carlo simulations of frustrated XY models on square and triangular lattices.