Relaxation behavior of fractal-cluster spin glasses

The relaxation behavior of spin glasses has been analyzed in the framework of the critical fractal-cluster model. It is found that the relaxation rate of the magnetization can be expressed as $\frac{\partial m}{\partial \ln t}\propto t^{-\frac{\beta }{z\nu }}\exp [-{\left(\frac{t}{{\tau }_{\xi }}\right)}^{\frac{\beta \delta }{z\nu }}]$, where $\beta$, $\delta$, $z$, $\nu$ are standard static and dynamic critical exponents and ${\tau }_{\xi }$ is the relaxation time of a characteristic cluster which diverges at the spin-glass freezing temperature $T_g$. The expression is valid through $T_g$ and is found to describe excellently the fundamental features of the relaxation in real spin glasses.