ZERO-TEMPERATURE SPIN DYNAMICS OF A RANDOM 2-DIMENSIONAL XY MODEL

We study the zero-temperature spin dynamics of a random-exchange two-dimensional XY model using both exact numerical methods and an approach based upon the coherent potential approximation (CPA). The model, which presents a mixed-phase to spin-glass phase transition, consists of a ferromagnetic host with nearest-neighbor bonds J to which one substitutes impurity bonds of strength -lambdaJ at concentration x. In both phases, the long-wavelength magnetic excitations of this system are spin waves with a linear spectrum. The x and lambda dependence of the spin-wave velocity is determined numerically by calculating the stiffness constant of the system with a new transfer-matrix algorithm. The stiffness constant and the spin-wave velocity decrease rapidly with increasing x. The two quantities are smooth across the phase boundary, and they saturate in the spin-glass phase. At shorter wavelengths, the q dependence of the energies and lifetimes of the spin waves in the ferromagnetic and spin-glass states differs qualitatively, reflecting the morphological differences that exist between the spin configurations characteristic of the two phases. Line shapes and linewidths depend strongly on the polarization of the excitations. Whereas out-of-plane modes stay propagative at all concentrations, in-plane ones are inhomogeneously broadened and are overdamped at long wavelengths. There is good overall agreement between the exact numerical results and those obtained using the CPA.