Dimensional crossover and universal roughness distributions in Barkhausen noise

We investigate the dimensional crossover of scaling properties of avalanches (domain-wall jumps) in a single-interface model, used for the description of Barkhausen noise in disordered magnets. By varying the transverse aspect ratio $A=L_y\mathrm{/}{L}_x$ of simulated samples, the system dimensionality changes from two to three. We find that perturbing away from $d=2$ is a relevant field. The exponent $\tau$ characterizing the power-law scaling of avalanche distributions varies between $1.06(1)$ for $d=2$ and $1.275(15)$ for $d=3$, according to a crossover function $f(x)$, $x\equiv (L_x^{-1}{)}^{\varphi }\mathrm{/}A$, with $\varphi =0.95(3)$. We discuss the possible relevance of our results to the interpretation of thin-film measurements of Barkhausen noise. We also study the probability distributions of interface roughness, sampled among successive equilibrium configurations in the Barkhausen noise regime. Attempts to fit our data to the class of universality distributions associated to $1\mathrm{/}{f}^{\alpha }$ noise give $\alpha \simeq 1-1.1$ for $d=2$ and 3 (provided that suitable boundary conditions are used in the latter case).