Experimental verification of activated critical dynamics in the d=3 random-field Ising model

Ac susceptibility studies of the d=3 random-field Ising-model (RFIM) system ${\mathrm{Fe}}_{0.46}$ ${\mathrm{Zn}}_{0.54}$ ${\mathrm{F}}_2$ in the 5×${10}^{\mathrm{-}3}$⩽ω/2π⩽${10}^5$ Hz frequency range show the ω scaling of the peak value [${\mathrm{\chi }}_{\mathrm{c}}^{\prime }$(ω)${]}_{\mathrm{p}}$ and the characteristic rounding temperature ${\mathrm{t}}^{\mathrm{*}}$(ω) are consistent with activated, but not conventional, dynamic scaling. We find [${\mathrm{\chi }}_{\mathrm{c}}^{\prime }$(χ)${]}_{\mathrm{p}}$∼log|log(ω/${\mathrm{\omega }}_0$)| and ${\mathrm{t}}^{\mathrm{*}}$(ω)∼|log(ω/${\mathrm{\omega }}_0$ ${\mathrm{|}}^{\mathrm{-}1/\mathrm{y}}$ with y=1.05±0.16 and ${\mathrm{\omega }}_0$≃${10}^8$ ${\mathrm{s}}^{\mathrm{-}1}$ in agreement with the random-exchange Ising-model (REIM) dynamic frequency at the REIM-to-RFIM crossover. The relation between these results and the Villain-Fisher theories is discussed.