RENORMALIZATION-GROUP STUDY OF THE COUPLED XY-ISING MODELS

The coupled and discretized XY-Ising models describing frustrated XY and Josephson-junction systems are studied by the discretized Migdal-Kadanoff renormalization-group approach. Both uniform and disordered systems are considered. The phase diagram of the uniform two-dimensional (2D) model generally agrees with the previous studies but existence of a new antiferromagnetic phase is predicted. The random-gauge XY-Ising model is introduced to describe two-dimensional disordered systems with a half-integer number of the average flux per plaquette. Finite-temperature reentrancy from the paramagnetic to ferromagnetic Ising phases is predicted for the 2D random-gauge systems. At T=0, the gauge glass and Ising spin-glass phases can coexist provided the coupling to the Ising degrees of freedom is less than a critical value. In the 3D case, the finite-temperature gauge glass phase can exist only provided the Ising subsystem is also ordered, either in the ferromagnetic or the spin-glass fashion. The chaotic behavior of two mixed phases (one of them is of gauge glass and Ising spin glass and the other one is of gauge glass and Ising ferromagnet) is studied at T=0. Within the discretization scheme the Lyapunov exponents are found to be different for these phases.