Thermally activated interface motion in a disordered ferromagnet

We investigate interface motion in disordered ferromagnets by means of Monte Carlo simulations. For small temperatures and driving fields a so-called creep regime is found and the interface velocity obeys an Arrhenius law. We analyze the corresponding energy barrier as well as the field and temperature dependence of the prefactor.Comment: accepted for publication in Computer Physics Communication

Dynamic effect of overhangs and islands at the depinning transition in two-dimensional magnets

With the Monte Carlo methods, we systematically investigate the short-time dynamics of domain-wall motion in the two-dimensional random-field Ising model with a driving field ?DRFIM?. We accurately determine the depinning transition field and critical exponents. Through two different definitions of the domain interface, we examine the dynamics of overhangs and islands. At the depinning transition, the dynamic effect of overhangs and islands reaches maximum. We argue that this should be an important mechanism leading the DRFIM model to a different universality class from the Edwards-Wilkinson equation with quenched disorderComment: 9 pages, 6 figure

Interface Motion in Disordered Ferromagnets

We consider numerically the depinning transition in the random-field Ising model. Our analysis reveals that the three and four dimensional model displays a simple scaling behavior whereas the five dimensional scaling behavior is affected by logarithmic corrections. This suggests that d=5 is the upper critical dimension of the depinning transition in the random-field Ising model. Furthermore, we investigate the so-called creep regime (small driving fields and temperatures) where the interface velocity is given by an Arrhenius law.Comment: some misprints correcte

Creep motion in a random-field Ising model

We analyze numerically a moving interface in the random-field Ising model which is driven by a magnetic field. Without thermal fluctuations the system displays a depinning phase transition, i.e., the interface is pinned below a certain critical value of the driving field. For finite temperatures the interface moves even for driving fields below the critical value. In this so-called creep regime the dependence of the interface velocity on the temperature is expected to obey an Arrhenius law. We investigate the details of this Arrhenius behavior in two and three dimensions and compare our results with predictions obtained from renormalization group approaches.Comment: 6 pages, 11 figures, accepted for publication in Phys. Rev.

The depinning transition of a driven interface in the random-field Ising model around the upper critical dimension

We investigate the depinning transition for driven interfaces in the random-field Ising model for various dimensions. We consider the order parameter as a function of the control parameter (driving field) and examine the effect of thermal fluctuations. Although thermal fluctuations drive the system away from criticality the order parameter obeys a certain scaling law for sufficiently low temperatures and the corresponding exponents are determined. Our results suggest that the so-called upper critical dimension of the depinning transition is five and that the systems belongs to the universality class of the quenched Edward-Wilkinson equation.Comment: accepted for publication in Phys. Rev.

Monte Carlo Dynamics of driven Flux Lines in Disordered Media

We show that the common local Monte Carlo rules used to simulate the motion of driven flux lines in disordered media cannot capture the interplay between elasticity and disorder which lies at the heart of these systems. We therefore discuss a class of generalized Monte Carlo algorithms where an arbitrary number of line elements may move at the same time. We prove that all these dynamical rules have the same value of the critical force and possess phase spaces made up of a single ergodic component. A variant Monte Carlo algorithm allows to compute the critical force of a sample in a single pass through the system. We establish dynamical scaling properties and obtain precise values for the critical force, which is finite even for an unbounded distribution of the disorder. Extensions to higher dimensions are outlined.Comment: 4 pages, 3 figure

Higher correlations, universal distributions and finite size scaling in the field theory of depinning

Recently we constructed a renormalizable field theory up to two loops for the quasi-static depinning of elastic manifolds in a disordered environment. Here we explore further properties of the theory. We show how higher correlation functions of the displacement field can be computed. Drastic simplifications occur, unveiling much simpler diagrammatic rules than anticipated. This is applied to the universal scaled width-distribution. The expansion in d=4-epsilon predicts that the scaled distribution coincides to the lowest orders with the one for a Gaussian theory with propagator G(q)=1/q^(d+2 \zeta), zeta being the roughness exponent. The deviations from this Gaussian result are small and involve higher correlation functions, which are computed here for different boundary conditions. Other universal quantities are defined and evaluated: We perform a general analysis of the stability of the fixed point. We find that the correction-to-scaling exponent is omega=-epsilon and not -epsilon/3 as used in the analysis of some simulations. A more detailed study of the upper critical dimension is given, where the roughness of interfaces grows as a power of a logarithm instead of a pure power.Comment: 15 pages revtex4. See also preceding article cond-mat/030146

Origin of the roughness exponent in elastic strings at the depinning threshold

Within a recently developed framework of dynamical Monte Carlo algorithms, we compute the roughness exponent $\zeta$ of driven elastic strings at the depinning threshold in 1+1 dimensions for different functional forms of the (short-range) elastic energy. A purely harmonic elastic energy leads to an unphysical value for $\zeta$. We include supplementary terms in the elastic energy of at least quartic order in the local extension. We then find a roughness exponent of $\zeta \simeq 0.63$, which coincides with the one obtained for different cellular automaton models of directed percolation depinning. The quartic term translates into a nonlinear piece which changes the roughness exponent in the corresponding continuum equation of motion. We discuss the implications of our analysis for higher-dimensional elastic manifolds in disordered media.Comment: 4 pages, 2 figure