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^-νHf(t), where H is the random-field amplitude and t is the time. At low temperature, νH=2 and f(t)=ln(tτ). At the transition temperature Tc0 of the pure system, νH1 and $f(t)=1$. The agreement with experiment is acceptable.