Anisotropy and anisotropy-triad dynamics in spin-glasses

We present a physical picture for the spin triad ($\hat{n}$,$\hat{p}$,$\hat{q}$) and anisotropy triad ($\hat{N}$,$\hat{P}$,$\hat{Q}$) introduced in our earlier work. A discussion of some of the experimental implications of anisotropy relaxation is then given, and it is argued, by citing examples of less complex systems with random anisotropy, that such relaxation is independent of the processes responsible for the time-dependent remanence associated with the spin-glass state. (It is suggested that increasing the spin dimensionality will shed light on this latter question.) The form of the anisotropy torque is considered, including global triad and global single-axis anisotropy; it is also shown how global averaging over local triad anisotropy can yield global single-axis anisotropy. Expressions are derived for the macroscopic dissipative coefficients in terms of time integrals of equilibrium correlation functions. Finally, it is shown, in the limit of vanishing anisotropy, that only the macroscopic modes contribute to the total magnetization and to the new spin-space rotation angle which we introduce in this paper.