Dynamics of one-dimensional Heisenberg spin glasses in the high-field limit.

Abstract

This paper reports the results of a study of the distribution and localization of the magnon modes in one-dimensional Heisenberg spin glasses with nearest-neighbor interactions. The analysis is limited to high fields and frequencies near the precession frequency. Both symmetric and asymmetric distributions of exchange interactions of the form P(J)\ensuremath{\propto}\ensuremath{\Vert}J${\mathrm{\ensuremath{\Vert}}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\alpha}}}$ (\ensuremath{\alpha}1) are treated in detail. The results of approximate calculations based on the coherent-exchange approximation are shown to be in good agreement with numerical data obtained by applying mode-counting techniques to arrays of ${10}^{7}$ spins. Particular emphasis is placed on the qualitative differences in the behavior that arise depending on whether the average values of ${\mathit{J}}^{\mathrm{\ensuremath{-}}1}$ and ${\mathit{J}}^{\mathrm{\ensuremath{-}}2}$ are zero, nonzero, or infinite.