Perturbation theory for ac-driven interfaces in random media

Abstract

We study D-dimensional elastic manifolds driven by ac forces in a disordered environment using a perturbation expansion in the disorder strength and the mean-field approximation. We find that for D ≤ 4 , perturbation theory produces nonregular terms that grow unboundedly in time. The origin of these nonregular terms is explained. By using a graphical representation we argue that the perturbation expansion is regular to all orders for D > 4. Moreover, for the corresponding mean-field problem we prove that ill-behaved diagrams can be resummed in a way that their unbounded parts mutually cancel. Our analytical results are supported by numerical investigations. Furthermore, we conjecture the scaling of the Fourier coefficients of the mean velocity with the amplitude of the driving force h .

Nonsteady dynamic properties of a domain wall for the creep state under an alternating driving field

“…Up to date, theoretical tools for describing the domain-wall motion are typically based on the Edwards-Wilkinson equation with quenched disorder (QEW) [6,[28][29][30][31][32]. With this equation, the dynamics properties for the creep state under a constant driving field or zero field have been well understood [33][34][35].…”

“…While experimental values of β vary from 0.2 to 0.65 in ultrathin ferromagnetic and ferroelectric films [20-22]. Hence, it remains much challenging to understand the creep exponent.Up to date, theoretical tools for describing the domain-wall motion are typically based on the Edwards-Wilkinson equation with quenched disorder (QEW) [6,[28][29][30][31][32]. With this equation, the dynamics properties for the creep state under a constant driving field or zero field have been well understood [33][34][35].…”

Mean-field theory for driven domain walls in disordered environments

“…[26], where the concept of waiting time distributions has been used. Moreover, the perturbation theory for ac-driven interfaces in random environments has been examined [27]. Further study of ac-driven elastic systems in disordered media has been devoted to vortex lattices [28] and structural defects in liquid crystals [29].…”