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Large-scale dynamical simulations of the three-dimensional XY spin glass

Large-scale simulations have been performed in the current-driven three-dimensional XY spin glass with resistively-shunted junction dynamics for sample sizes up to $64^3$. It is observed that the linear resistivity at low temperatures tends to zero, providing a strong evidence of a finite temperature phase-coherence (i.e. spin-glass) transition. Dynamical scaling analysis demonstrates that a perfect collapse of current-voltage data can be achieved. The obtained critical exponents agree with those in equilibrium Monte Carlo simulations, and are compatible with those observed in various experiments on high-T$_c$ cuprate superconductors. It is suggested that the spin and the chirality order simultaneously. A genuine continuous depinning transition is found at zero temperature. For low temperature creep motion, critical exponents are evaluated, and a non-Arrhenius creep motion is observed in the low temperature ordered phase. It is proposed that the XY spin glass gives an effective description of the transport properties in high-T$_c$ superconductors with d-wave symmetry.