Depinning phase transition in two-dimensional clock model with quenched randomness

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 $\zeta \mathrm{\ne }{\zeta }_{loc}\mathrm{\ne }{\zeta }_s$ and ${\zeta }_{loc}\mathrm{\ne }1$. More importantly, we find that the transition field and critical exponents change with the initial orientations of the magnetization of the two ordered domains.