Numerical simulations based on Monte Carlo dynamics are used to investigate the resistivity behavior of granular superconductors containing a random distribution of pi junctions, as in superconducting materials with d-wave symmetry. The presence of pi junctions leads to quenched in circulating currents (chiralities) and to chiral glass behavior at low temperatures, even without an external magnetic field. An XY spin glass model in the phase representation is used to determine the current-voltage characteristics and critical exponents of the resistivity transition. In two dimensions, the linear resistivity is nonzero at finite temperatures and the dynamic scaling analysis of the nonlinear resistivity is consistent with a phase transition at zero temperature. In three dimensions, we find a transition at finite temperatures below which the linear resistivity vanishes and the corresponding critical exponents are determined from the scaling analysis. The results are in good agreement with Langevin simulations in the phase representation. The dynamic exponent z is significantly different from previous results obtained in the vortex representation.

The critical behavior of zero-temperature superconducting transitions which can occur in disordered two-dimensional Josephson-junction arrays are investigated by Monte Carlo calculation of ground-state excitation energies and dynamical simulation of the current-voltage characteristics at nonzero temperatures. Two models of arrays in an applied magnetic field are considered: random dilution of junctions and random couplings with half-ux quantum per plaquette f = 1/2. Abovea critical value of disorder, finite-size scaling of the excitation energies indicates a zero-temperature transition and allows an estimate of the critical disorder and the thermal correlation length exponent characterizing the transition. Current-voltage scaling is consistent with the zero-temperature transition. The linear resistance is nonzero at finite temperatures but nonlinear behavior sets in at a characteristic current density determined by the thermal critical exponent. The zero-temperature transition provides an explanation of the washing out of structure for increasing disorder at f = 1/2 while it remains for f = 0, observed experimentally in supercondoucting wire networks.