Universality beyond power laws and the average avalanche shape

The study of critical phenomena and universal power laws has been one of the central advances in statistical mechanicsduring the second half of the past century, explaining traditional thermodynamic critical points1, avalanche behaviour near depinning transitions2, 3 and a wide variety of other phenomena4. Scaling, universality and the renormalization group claim to predict all behaviour at long length and timescales asymptotically close to critical points. In most cases, the comparison between theory and experiments has been limited to the evaluation of the critical exponents of the power-law distributions predicted at criticality. An excellent area for investigating scaling phenomena is provided by systems exhibiting crackling noise, such as the Barkhausen effect in ferromagnetic materials5. Here we go beyond power-law scaling and focus on the average functional form of the noise emitted by avalanches—the average temporal avalanche shape4. By analysing thin permalloy films and improving the data analysis methods, our experiments become quantitatively consistent with our calculation for the multivariable scaling function in the presence of a demagnetizing field and finite field-ramp rate.