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

Abstract

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 ${H}^{{\ensuremath{-}\ensuremath{\nu}}_{H}}f(t)$, where $H$ is the random-field amplitude and $t$ is the time. At low temperature, ${\ensuremath{\nu}}_{H}=2$ and $f(t)=\mathrm{ln}(\frac{t}{\ensuremath{\tau}})$. At the transition temperature ${T}_{c0}$ of the pure system, ${\ensuremath{\nu}}_{H}\ensuremath{\simeq}1$ and $f(t)=1$. The agreement with experiment is acceptable.