Critical behavior of the magnetization of ad=3random-field ising system

Optical Faraday rotation was used to measure the uniform "dc" magnetization $M$ versus $T$ in the random-field Ising model (RFIM) system ${\mathrm{Fe}}_{0.47}$ ${\mathrm{Zn}}_{0.53}$ ${\mathrm{F}}_2$ in fields $0.2\le H\le 1.9$ T. Both ${\left(\frac{\delta M}{\delta T}\right)}_H$ and ${\left(\frac{\delta M}{\delta H}\right)}_T$ diverge as $H^y\ln \mathrm{}\left|t\right|\mathrm{}$, as does the specific heat. Significantly different amplitude exponents were measured, $y\sim 0.6 \mathrm{and} 1.0$, respectively, confirming scaling-theory predictions. The observed rounding of the phase transition below $\mathrm{}\left|t\right|\mathrm{}\sim 1\times {10}^{-3\mathrm{}}$, at $H=1.0\mathrm{}$ T, results from extreme slowing down of the RFIM critical fluctuations consistent with extrapolating ${\chi }^{\prime }\left(\omega \right)$ studies to a measurement time scale $\tau =\frac{1}{\omega }\sim 100$ s.