Large-scale Monte Carlo simulations for the depinning transition in Ising-type lattice models

Abstract

With the developed "extended Monte Calro" (EMC) algorithm, we have studied the depinning transition in Ising-type lattice models by extensive numerical simulations, taking the random-field Ising model with a driving field and the driven bond-diluted Ising model as examples. In comparison with the usual Monte Carlo method, the EMC algorithm exhibits greater efficiency of the simulations. Based on the short-time dynamic scaling form, both the transition field and critical exponents of the depinning transition are determined accurately via the large-scale simulations with the lattice size up to L = 8 912, significantly refining the results in earlier literature. In the strong-disorder regime, a new universality class of the Ising-type lattice model is unveiled with the exponents β = 0.304(5), ν = 1.32(3), z = 1.12(1), and ζ = 0.90(1), quite different from that of the Edwards-Wilkinson equation.

Dynamic depinning phase transition in magnetic thin film with anisotropy

“…includes those in both z and y directions, F(t) is proportional to the correlation length ξ(t) [21],…”

“…On the other hand, the tilt symmetry characterized by the scaling law (2−ζ)ν=1 is an interesting property of the QEW equation, which relates the roughness length scale and the correlation length scale at the depinning phase transition. This tilt symmetry is violated in the Monte Carlo simulation of the Ising model, possibly due to the overhangs and islands [21]. However, (2−ζ) ν=0.98 (3) indicates that the tilt symmetry holds for the LLG equation of the Heisenberg model with anisotropy.…”

“…There have been theoretical efforts with the quenched Edwards-Wilkinson (QEW) equation and the Monte Carlo simulation, to understand the depinning phase transition of the domain-wall motion [15][16][17][18][19][20][21]. The QEW equation is a simple phenomenological model, where a domain wall is considered to be an elastic string, and detailed microscopic structures and interactions of the materials are not concerned.…”

Spin-reorientation critical dynamics in the two-dimensional XY model with a domain wall

“…Driven by a constant external field in the presence of the quenched disorder, a pinning-depinning dynamic transition occurs at zero temperature, separating the regimes of static pinning and friction-limited viscous sliding [22][23][24]. At low temperatures, the sharp depinning transition is softened, and a thermally activated creep motion appears [25][26][27][28].…”

“…Practically, predicting and controlling the movements of the domain walls play a crucial role in designing new classes of magnetic devices. Moreover, the dynamic approaches can be developed to study the pinning-depinning and other dynamic phase transitions of domain walls at zero or low temperatures, understand the non-stationary properties of the dynamic systems, and determine the static and dynamic exponents as well as the transition points [18,22,24,25]. However, most of efforts were focused on the 180 • domain wall in earlier studies of domain dynamics, and the dynamics of non-180 • one was rarely referred.…”