Anisotropy-Triad Dynamics in Spin-Glasses

Abstract

In Heisenberg spin-glasses, the orientation of a state is specified by a reference spin triad ($\stackrel{^}{n}, \stackrel{^}{p}, \stackrel{^}{q}$), and its anisotropy is specified by a rotation $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\psi}}$ of this state away from its equilibrium orientation. Rotation of ($\stackrel{^}{n}, \stackrel{^}{p}, \stackrel{^}{q}$) by $\ensuremath{-}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\psi}}$ defines an anisotropy triad ($\stackrel{^}{N}, \stackrel{^}{P}, \stackrel{^}{Q}$), whose dynamics is derived. This dynamics is exclusively dissipative, consistent with torque and ESR measurements. Analogy to ordinary glasses suggests a Vogel-Fulcher law for the associated relaxation time.