We present a microscopical model of the domain wall motion through a d
isordered medium. Unlike a previous phenomenological model, which expl
ains most of the experimental data, the disorder is supposed to be unc
orrelated. The dynamical equation of the motion has a upper critical d
imension of 3, so that a mean field description is suitable to describ
e soft magnetic materials. It is shown that the correlation of the dis
order is a consequence of the nature of the magnetic interactions and
not an intrinsic property of the materials. The mean field critical ex
ponents well agree with the phenomenological model and with simulated
and experimental data.