Dynamical implications of sample shape for avalanches in 2-dimensional random-field Ising model with saw-tooth domain wall

Abstract

We study dynamics of an injected domain wall (DW) in 2-dimensional disordered ferromagnets with different sample shapes using random-field Ising model on a square lattice rotated by 45 degrees. The saw-tooth DW of the length $L_x$ is created along one side and swept through the sample by slow ramping of the external field until the complete magnetisation reversal and the wall annihilation at the open top boundary at a distance $L_y$. By fixing the number of spins $N=L_x\times L_y=10^6$ and the random-field distribution above the critical disorder, we vary the ratio $L_x/L_y\in[1/16,16]$. The periodic boundary conditions are applied in the y-direction so that these ratios comprise different samples, i.e., surfaces of cylinders with the changing perimeter $L_x$ and height $L_y$. We analyse the avalanches of the DW slips between following field updates, and the multifractal structure of the magnetisation fluctuation time series. Our findings are that the domain-wall lengths materialised in different sample shapes have an impact on the dynamics at all scales.