  With Monte Carlo simulations, we systematically investigate the depinning
phase transition in the two-dimensional driven random-field clock model. Based
on the short-time dynamic approach, we determine the transition field and
critical exponents. The results show that the critical exponents vary with the
form of the random-field distribution and the strength of the random fields,
and the roughening dynamics of the domain interface belongs to the new subclass
with $\zeta \neq \zeta_{loc} \neq \zeta_s$ and $\zeta_{loc} \neq 1$. More
importantly, we find that the transition field and critical exponents change
with the initial orientations of the magnetization of the two ordered domains.
