  We present a line-based model of transverse domain walls in thin magnetic
strips, to study the effect of bulk disorder on the domain wall dynamics within
the thermally activated creep regime. The creep velocity is found to exhibit a
non-linear dependence on both applied magnetic fields and electric currents,
characterized by similar creep exponents for both forms of the external drive.
We discuss briefly the significance of the inherently stochastic thermally
activated domain wall motion from the point of view of spintronics
applications, where it generally is essential to be able to control the domain
wall displacement in a deterministic manner.
