  Based on the Hamiltonian equation of motion of the $\phi^4$ theory with
quenched disorder, we investigate the depinning phase transition of the
domain-wall motion in two-dimensional magnets. With the short-time dynamic
approach, we numerically determine the transition field, and the static and
dynamic critical exponents. The results show that the fundamental Hamiltonian
equation of motion belongs to a universality class very different from those
effective equations of motion.
