Faculty of Physics, University of Belgrade, POB 368, 11001 Belgrade, Serbia.
Centre de Recerca Matematica, Edifici C, Campus Bellaterra, E-08193 Bellaterra, Catalonia, Spain; Barcelona Graduate School of Mathematics (BGSMath), Edifici C, Campus Bellaterra, E-08193 Barcelona, Spain; and Facultat de Matemàtiques i Informàtica, Universitat de Barcelona, Gran Via de les Corts Catalanes, 585, E-08007 Barcelona, Spain.
Phys Rev E. 2018 Jan;97(1-1):012109. doi: 10.1103/PhysRevE.97.012109.
We present extensive numerical studies of the crossover from three-dimensional to two-dimensional systems in the nonequilibrium zero-temperature random-field Ising model with metastable dynamics. Bivariate finite-size scaling hypotheses are presented for systems with sizes L×L×l which explain the size-driven critical crossover from two dimensions (l=const, L→∞) to three dimensions (l∝L→∞). A model of effective critical disorder R_{c}^{eff}(l,L) with a unique fitting parameter and no free parameters in the R_{c}^{eff}(l,L→∞) limit is proposed, together with expressions for the scaling of avalanche distributions bringing important implications for related experimental data analysis, especially in the case of thin three-dimensional systems.
我们呈现了大量的数值研究，探讨了非平衡零温随机场伊辛模型中具有亚稳动力学的三维到二维系统的交叉。对于大小为 L×L×l 的系统，提出了二元有限尺寸标度假设，这些假设解释了从二维（l=const，L→∞）到三维（l∝L→∞）的尺寸驱动的临界交叉。我们提出了一个有效的临界无序模型 R_{c}^{eff}(l,L)，该模型具有一个独特的拟合参数，在 R_{c}^{eff}(l,L→∞)极限下没有自由参数，并且还提出了关于雪崩分布标度的表达式，这对相关的实验数据分析具有重要意义，特别是在三维系统较薄的情况下。
