Anomalous dynamics in two- and three- dimensional Heisenberg-Mattis spin glasses

We investigate the spectral and localization properties of unmagnetized Heisenberg-Mattis spin glasses, in space dimensionalities $d=2$ and 3, at T=0. We use numerical transfer-matrix methods combined with finite-size scaling to calculate Lyapunov exponents, and eigenvalue-counting theorems, coupled with Gaussian elimination algorithms, to evaluate densities of states. In $d=2$ we find that all states are localized, with the localization length diverging as $\omega^{-1}$, as energy $\omega \to 0$. Logarithmic corrections to density of states behave in accordance with theoretical predictions. In $d=3$ the density-of-states dependence on energy is the same as for spin waves in pure antiferromagnets, again in agreement with theoretical predictions, though the corresponding amplitudes differ.