Hamiltonian equation of motion and depinning phase transition in   two-dimensional magnets
  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. 
R. H. Dong, B. Zheng and N. J. Zhou
cond-mat.dis-nn cond-mat.stat-mech