We investigate the criticality of the athermal, nonequilibrium random field Ising model on three-dimensional lattices with coordination number z=3. Using state-of-the-art numerical simulations and finite-size scaling analysis, we address a longstanding theoretical question: the absence of disorder-induced critical behavior in systems with low coordination numbers. Our results provide compelling evidence that the model lacks nontrivial criticality, as indicated by the disorder dependence of the effective critical magnetic field, the average size of spanning avalanches, and the scaling collapses of avalanche parameters. Extensive simulations, including both regular lattices and systems with preset interfaces, reveal that coordination number and lattice dimensionality are the key factors governing critical behavior. These findings not only deepen our understanding of the distinctions between nonequilibrium and equilibrium critical phenomena in disordered systems but also offer insights relevant to the design of self-assembled materials with unique structural properties.

中文翻译：

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关于无序铁磁体模型在低配位数的 3D 晶格中的临界度


我们研究了无热、非平衡随机场 Ising 模型在配位数 z=3 的三维晶格上的重要性。使用最先进的数值模拟和有限尺寸缩放分析，我们解决了一个长期存在的理论问题：在低配位数的系统中不存在无序诱导的临界行为。我们的结果提供了令人信服的证据，证明该模型缺乏非平凡的临界性，正如有效临界磁场的无序依赖性、跨越雪崩的平均大小以及雪崩参数的缩放崩溃所表明的那样。广泛的仿真，包括常规晶格和具有预设接口的系统，表明配位数和晶格维数是控制关键行为的关键因素。这些发现不仅加深了我们对无序系统中非平衡和平衡临界现象之间区别的理解，而且还为具有独特结构特性的自组装材料的设计提供了相关的见解。