Spin activity correlations in driven disordered systems

Abstract

We study the spatio-temporal correlations in the spin flipping activities of the disordered systems realized within the frame of the field-driven three-dimensional zero-temperature nonequilibrium random field Ising model. Our results for the spatial activity correlations reveal that the rate-dependent scaling holds in the full range of rate regimes provided that the system parameters satisfy the finite-size and rate-dependent scaling conditions. Temporal activity correlations show high sensitivity to the driving, allowing the collapsing of waiting time distributions only in the limit of slow driving rates. These findings, based on extensive numerical simulations of large systems, reliably demonstrate the observed behavior and could be relevant for studies on various, particularly experimental, nonequilibrium systems driven at finite rates.

Dimensional crossover in driving-rate induced criticality on the hysteresis-loop of disordered ferromagnetic systems

“…Correlation functions of studied spin-flip events for small driving rates decrease with the inter-spin distance in an adiabatic way, but are being divided into two families according to the system thickness with separation occurring at the transient thickness. Region after the cutoff is having the plateau, observed previously in equilateral systems with finite driving [32]. With further increase of driving rate the spanning-induced plateau occurs, with the variable slopes in the range prior to plateau due to the presence of both small 3D avalanches and 2D ones.…”

“…We see that for slow and intermediate driving regimes they are fairly symmetric for all system thicknesses, while for fast rates presented in the right panel, due to the superposition of simultaneously propagating avalanches, we see the flattening of their shapes. This effect was also observed in equilateral field-driven systems [32].…”

“…For the sake of simplicity, in what follows we will dub G t int (x; R, Ω, L, l) as correlation function and denote it as G int (x). The correlation function G int (x) exhibits similar rate dependency as was shown in pure equilateral 3D systems [32], with some alterations in the transition from 3D to 2D with the systematic change of system thickness l. In figure 7 (top row panels), we show these correlation functions covering the full range of thickness in the representative driving regimes. In the slow driving regime we see the characteristic shapes, adiabatically-like decreasing with the inter-spin distance x, followed by the post-cutoff plateaus occurring in the range of big spin distances.…”

“…Triggered activity event correlation function defined and studied in [31,32] for the systems driven with a finite driving rate, measures the correlations between the pairs of spins belonging to the same activity event and being separated by a distance x. This function is estimated as…”

“…This was followed by the studies [18,[21][22][23] treating the nonequilateral systems within the framework of the same model, considering the effects of aspect ratio [24] and different underlying lattice geometry [25,26], however also on systems driven adiabatically. On the other hand, several studies on systems driven with the finite driving rate have been reported recently, but on equilateral systems [27][28][29][30][31][32].…”