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 $zeta eq zeta_{loc} eq zeta_s$ and $zeta_{loc} eq 1$. More importantly, we find that the transition field and critical exponents change with the initial orientations of the magnetization of the two ordered domains.

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 $zeta eq zeta_{loc} eq zeta_s$ and $zeta_{loc} eq 1$. 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.

Dynamic relaxation of topological defect at Kosterlitz-Thouless phase transition

With Monte Carlo methods we study the dynamic relaxation of a vortex state at the Kosterlitz-Thouless phase transition of the two-dimensional XY model. A local pseudo-magnetization is introduced to characterize the symmetric structure of the dynamic systems. The dynamic scaling behavior of the pseudo-magnetization and Binder cumulant is carefully analyzed, and the critical exponents are determined. To illustrate the dynamic effect of the topological defect, similar analysis for the the dynamic relaxation with a spin-wave initial state is also performed for comparison. We demonstrate that a limited amount of quenched disorder in the core of the vortex state may alter the dynamic universality class. Further, theoretical calculations based on the long-wave approximation are presented.