ac Susceptibility Study of thed=3Random-Field Critical Dynamics

The dynamic critical behavior in a $d=3\mathrm{}$ random-field Ising-model system is studied with ac susceptibility $\chi \left(\omega \right)$ techniques on ${\mathrm{Fe}}_{0.46}$ ${\mathrm{Zn}}_{0.54}$ ${\mathrm{F}}_2$. Extraordinary critical slowing down is seen in the $\omega$ dependence of ${\chi }^{\prime }\left(\omega \right)$ at very low frequencies. In the range 2 Hz to 8.5 kHz, the peak value ${\left[{\chi }_c^{\prime }\right(\omega \left)\right]}_p$ decreases and the width $t^{*}\left(\omega \right)$ increases with increasing $\omega$. A conventional dynamicscaling interpretation with $t^{*}\left(\omega \right)\sim {\omega }^{\frac{1}{z\nu }}$ gives ${\left[{\chi }_c^{\prime }\right(\omega \left)\right]}_p\sim \left|\ln \omega \right|$ and yields $z\nu \simeq 14$. An equally good fit is obtained with $t^{*}\left(\omega \right)\sim {\left|\ln \omega \right|}^{-1\mathrm{}}$ and ${\left[{\chi }_c^{\prime }\right(\omega \left)\right]}_p\sim \ln \left|\ln \omega \right|$, consistent with an activated dynamic scaling.