Dynamical susceptibility of spin glasses in the fractal cluster model

We study the dynamical susceptibility $\chi$ of spin glasses above the critical temperature using a fractal cluster model. We derive scaling relations for the zero-field limit of the real and imaginary parts of $\chi$ which are general since they do not depend on a particular relaxation model. Comparison to data on ${\mathrm{Eu}}_{0.4}$ ${\mathrm{Sr}}_{0.6}$S yields critical exponents in good agreement with independent determinations. We discuss the different criteria which have been used to extract the critical relaxation time ${\tau }_{\xi }$ from experimental $\chi \text{'}\mathrm{s}$. The smallness of the ratio $\frac{\beta }{\nu z}$ between critical exponents in the spin-glass problem justifies the approximations used to interpret and relate experimental data, for example, with the equation ${\chi }^{\prime \prime }=-\frac{\pi d{\chi }^{\prime }}{2d\ln \omega }$.