Numerical studies of spin-wave dynamics in Heisenberg spin-glasses

Abstract

We outline the numerical techniques used in calculating the one-magnon zero-temperature dynamic structure factor of a Heisenberg spin-glass. We employ equation-of-motion methods to study the dynamics of the Edwards-Anderson model where the exchange integral between nearest neighbors has a Gaussian distribution with zero mean and no correlation between different bonds. Numerical results are presented for a 16 × 16 × 16 simple cubic lattice with periodic boundary conditions. No evidence is found for long-wavelength propagating modes. A fit to the data suggests that at small $q$ the structure factor is peaked at $E=0\mathrm{}$. The methods are completely general and can be applied to other Heisenberg systems provided the exchange integrals and equilibrium spin orientations of the corresponding classical Hamiltonian are available as input.