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 , and the system response is size-independent. Between the foregoing two lies the domain of transitional disorders vanishing in the thermodynamic limit. In this domain, not recognized in the literature so far, all types of spanning avalanches exist, whereas for R < R _c only the avalanches spanning all three dimensions are present. Like for R < 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 < 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.

我们分析了有限大小L的等边立方晶格上的非平衡非热随机场伊辛模型（RFIM），并显示了整个无序范围都由三个不同的域组成，其中模型表现出不同的缩放行为。第一个域包含的扰动R的值低于临界扰动R _c，当系统受外部磁场驱动时，几乎肯定会出现跨越雪崩。对于规模依赖性有效疾病以上的疾病，跨越性的雪崩变得不太可能发生，并且系统反应与大小无关。在上述两个之间是过渡性疾病的领域在热力学极限中消失。在这个领域中，迄今为止尚无文献记载，存在所有类型的跨越雪崩，而对于R < R _c，仅存在跨越所有三个维度的雪崩。像R < R _c一样，数据折叠仅适用于（1- R _c / R）L ^{1 / ν} 值相同的分布，但是与R < R _c情况相比，通用缩放函数有所不同。ν是相关长度指数。前述发现来自对L 2048系统使我们能够提出一些RFIM临界指数和非通用临界参数的修改值，以及通用缩放函数的解析形式以及磁化强度和磁场强度的不同定义。