Universality class of the depinning transition in the two-dimensional   Ising model with quenched disorder
  With Monte Carlo methods, we investigate the universality class of the depinning transition in the two-dimensional Ising model with quenched random fields. Based on the short-time dynamic approach, we accurately determine the depinning transition field and both static and dynamic critical exponents. The critical exponents vary significantly with the form and strength of the random fields, but exhibit independence on the updating schemes of the Monte Carlo algorithm. From the roughness exponents $\zeta, \zeta_{loc}$ and $\zeta_s$, one may judge that the depinning transition of the random-field Ising model belongs to the new dynamic universality class with $\zeta \neq \zeta_{loc}\neq \zeta_s$ and $\zeta_{loc} \neq 1$. The crossover from the second-order phase transition to the first-order one is observed for the uniform distribution of the random fields, but it is not present for the Gaussian distribution. 
X. P. Qin, B. Zheng and N. J. Zhou
physics.comp-ph cond-mat.dis-nn cond-mat.stat-mech