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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.
Using high-precision Monte-Carlo simulations based on a parallel version of the Wang-Landau algorithm and finite-size scaling techniques we study the effect of quenched disorder in the crystal-field coupling of the Blume-Capel model on the square lat
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
We present several methods, which utilize symplectic integration techniques based on two and three part operator splitting, for numerically solving the equations of motion of the disordered, discrete nonlinear Schrodinger (DDNLS) equation, and compar
We consider the Ising model on the square lattice with biaxially correlated random ferromagnetic couplings, the critical point of which is fixed by self-duality. The disorder represents a relevant perturbation according to the extended Harris criteri
We use large-scale Monte Carlo simulations to test the Weinrib-Halperin criterion that predicts new universality classes in the presence of sufficiently slowly decaying power-law-correlated quenched disorder. While new universality classes are reason