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 finitesize 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 −1, as energy →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.