Ising domain wall in a random pinning potential

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Abstract
A continuum interface model is constructed to study the low-temperature properties of an Ising domain wall in a weak random pinning potential, which preserves the symmetry of the order parameter locally. The statistical width of the domain wall and its surface tension are computed by three methods: simple energy accounting, dimensional arguments, and approximate renormalisation-group calculations. All three methods yield a positive interface tension for d>1 as for pure thermal disorder. Quenched randomness, however, roughens the interface for d<or=5. For the model under consideration, the author does not find a depinning transition or a qualitative change of the roughening at non-zero temperatures, respectively, in contrast to other authors. Depinning can however be achieved by external perturbations such as electric fields or external stresses.