Fig. 2: Avalanche statistics for disorder strength Rx = 0.5J from zero temperature simulations.
The response of the magnetization to rotating driving field often proceeds via avalanches, in which there is a discontinuous jump in the magnetization δM in response to a small change δϕ of the driving field angle. a Statistics of largest avalanches. In a, we plot the size of the largest avalanche \(| \delta {\bf{M}}{| }_{\max }\) per limit cycle at each rotating field strength, disorder averaged, for a range of system sizes. b Statistics of second moment of avalanches. b shows the disorder average of the second moment δM of the avalanche size distribution where the error bars are the standard deviation over the disorder average as described in the text. The brackets \(<\ > \) denote an average over the limit cycle, and the overbar denotes a disorder average. By both of these measures, the size of the avalanches grows with system size implying divergent fluctuations at a critical field strength in the thermodynamic limit. The vertical bars in both panels mark the peak value from a running 3-point average. Within the resolution of the plot in a, these values are coincident for sizes N = 80 × 80 and N = 100 × 100, and for sizes N = 128 × 128 and N = 160 × 160. In b, the peak values are coincident for sizes N = 64 × 64 and N = 160 × 160.
