Kinetics of phase ordering in the two-dimensional coupled XY-Ising model

The ordering kinetics of a coupled XY-Ising model on a two-dimensional square lattice quenched from a disordered state to a low-temperature ordered phase is investigated via Monte Carlo dynamical simulations. The decay process of the two types of topological defects (point vortices and line defects of Ising domain walls) and the interaction between them controls the long-time dynamics of the ordering. In particular, the decoupling of XY degrees of freedom across Ising domain walls leads to the pinning of vortices near the walls, which considerably slows down the growth of XY order: it shows a power-law growth in time with the exponent phi(XY)similar or equal to 0.38. This vortex pinning also appears to give rise to a stretched exponential relaxation in the XY autocorrelation function. The dynamic scaling for both XY and Ising order parameters in the presence of multiple length scales is discussed.