Nonequilibrium "Critical" Exponents in the Random-Field Ising Model

The lower critical dimension for a random-field Ising model cooled from the paramagnetic region is found to be 4, although it is 2 at equilibrium. The coherence length $R$ is proportional to $H^{{-\nu }_H}f\left(t\right)\mathrm{}$, where $H$ is the random-field amplitude and $t$ is the time. At low temperature, ${\nu }_H=2\mathrm{}$ and $f\left(t\right)=\ln \left(\frac{t}{\tau }\right)$. At the transition temperature $T_{c0}$ of the pure system, ${\nu }_H\simeq 1$ and $f\left(t\right)=1\mathrm{}$. The agreement with experiment is acceptable.