Disorder-induced critical phenomena in hysteresis: Numerical scaling in three and higher dimensions

Abstract

We present numerical simulations of avalanches and critical phenomena associated with hysteresis loops, modeled using the zero-temperature random-field Ising model. We study the transition between smooth hysteresis loops and loops with a sharp jump in the magnetization, as the disorder in our model is decreased. In a large region near the critical point, we find scaling and critical phenomena, which are well described by the results of an ǫ expansion about six dimensions. We present the results of simulations in 3, 4, and 5 dimensions, with systems with up to a billion spins (1000 3 ).

Random-Field Ising Models of Hysteresis

“…Clearly in neither case is all the data collapsing onto a single curve. This would be distressing, were it not for the fact that this also occurs in 12 This section follows closely the presentation in (28). mean field theory (43) at a similar distance to the critical point.…”

“…1/σ is associated with the cutoff in the power law distribution of avalanche sizes integrated over the field H, while τ + σβδ gives the slope of that distribution. τ is obtained from the binned avalanche size distribution collapses (28). d + β/ν is obtained from avalanche correlation collapses and β/ν from magnetization discontinuity collapses.…”

“…The bottom figure 18 shows the integrated avalanche correlation curves collapse in 3 dimensions for L = 320 and R > R c . The exponent ν is obtained from such collapses by extrapolating to R = R c as was done for other collapses (43). The exponent β/ν can be obtained from these collapses too, but we found it better to use the jump in magnetization (28), which near the critical point involves several spanning avalanches.…”

“…The exponent ν is obtained from such collapses by extrapolating to R = R c as was done for other collapses (43). The exponent β/ν can be obtained from these collapses too, but we found it better to use the jump in magnetization (28), which near the critical point involves several spanning avalanches. Recent work (46; 47; 48) suggests that the jump in magnetization may be dominated by only one of these spanning avalanches, and their work suggests that there may be two exponents related to our β, one substantially larger (their β c ∼ 0.15±0.08).…”

Finite-size scaling analysis of the avalanches in the three-dimensional Gaussian random-field Ising model with metastable dynamics

“…[10][11][12][13][14][15] Two of the most well-studied properties are the number of avalanches N( ) and the distribution D(s; ) of avalanche sizes s along half a hysteresis loop. For large amounts of disorder ( Ͼ c ) the loops look smooth and continuous.…”