Scaling domains in the nonequilibrium athermal random field Ising model of finite systems

Abstract

We analyze the nonequilibrium athermal random field Ising model (RFIM) at equilateral cubic lattices of finite size L and show that the entire range of disorder consists of three distinct domains in which the model manifests different scaling behaviour. The first domain contains the values of disorder R that are below the critical disorder R c where the spanning avalanches almost surely appear when the system is driven by the external magnetic field. The spanning avalanches become unlikely for disorders above the size-dependent effective disorder R c eff ( L ) &gt; R c , and the system response is size-independent. Between the foregoing two lies the domain of transitional disorders <?CDATA ${R}_{\mathrm{c}}{< }R{ R c &lt; R &lt; R c eff ( L ) vanishing in the thermodynamic limit. In this domain, not recognized in the literature so far, all types of spanning avalanches exist, whereas for R &lt; R c only the avalanches spanning all three dimensions are present. Like for R &lt; R c the data collapsing is possible only for distributions having the same value of (1 − R c/R)L 1/ν , however with different universal scaling functions than in R &lt; R c case; ν is the correlation length exponent. The foregoing findings follow from the extensive simulations of L ⩽ 2048 systems enabling us to propose modified values of some of the RFIM critical exponents and nonuniversal critical parameters as well as the analytic forms of universal scaling functions and different definitions of reduced magnetization and reduced magnetic field.

Spin activity correlations in driven disordered systems

“…The zero-temperature (i.e. athermal) nonequilibrium version of the random field Ising model (ZT NEQ RFIM) [9][10][11][12][13][14][15] is a typical framework for disordered spin systems that experience the avalanche-like dynamics/relaxation when driven by the time-varying external magnetic field. As was previously found [16], three distinctive regimes for the driving at finite rates can be identified: slow, intermediate and fast rate regime.…”

“…As was previously found [16], three distinctive regimes for the driving at finite rates can be identified: slow, intermediate and fast rate regime. When the change of the external field is very slow, similarly as in the adiabatic case [13,15,17,18], avalanches propagate individually, well separated in time, which allows statistical interpretation of distributions of their parameters (such as size and duration). However, in most of experimental realizations the driving rate is finite [19,20].…”

The effects of external noise on threshold induced correlations in ferromagnetic systems

“…Our results are obtained in extensive simulations of system sizes up to L = 1024 for disorders R surpassing the effective critical disorder R eff c (L) which provides only the nonspanning avalanches which are mostly encountered in experiments, see [41]. The results gathered from the simulations were analyzed using the proprietary programs coded in Fortran, Visual Basic and Wolfram Mathematica.…”

“…In order to model and explain the Barkhausen noise that emerges when the ferromagnetic sample is driven by varying external magnetic field, a number of theoretical models were developed [24][25][26][27][28][29][30][31][32][33][34]. One of the most prominent appears to be the random field Ising model (RFIM), that has been extensively studied in the past few decades [35][36][37][38][39][40][41]. Renormalization group approach has brought certain answers regarding the RFIM critical behavior, but it turned out to be a rather difficult task.…”

“…This model has been studied numerically in a lot of papers. Its critical behavior and scaling laws in the case of equilateral lattices were investigated in [41,[50][51][52][53][54][55][56][57], whilst recently the systems with different geometry were studied in [58][59][60][61][62] together with the impact of lattice topology on its criticality [63][64][65][66][67].…”