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

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

2006-03-02

arxiv.org/abs/cond-mat/0603043v1

Physical Review B 73, 214421 (2006)

Physics

Condensed Matter

Statistical Mechanics

RevTeX4, 9 pages, 9 .eps figures

Scientific paper

10.1103/PhysRevB.73.214421

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.

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