Interface roughening and random-field instabilities in Ising systems in three or less dimensions

Abstract

The ferromagnetically ordered state of random-field Ising systems for dimensionalities $d<~3$ is shown to be unstable with respect to domain formation, if the field-induced domain interface roughness is taken into account. For $d=3\mathrm{}$, the interface exhibits a "wiggly" structure on all length scales intermediate between the correlation length and the domain size. This instability, which follows from the assumed random-field-induced roughening, makes the lower critical dimension, $d_l=3\mathrm{}$, consistent with the change of the effective dimensionality by 2 for the random-field model. Experimental consequences of these results are indicated.