2-D雪崩的奇怪缩放：固化小面，并在较低的临界尺寸中缩放
Weird scaling for 2-D avalanches: Curing the faceting, and scaling in the lower critical dimension
摘要：
非平衡无规场伊辛模型是一个研究较多的模型，但仍存在一些问题。在两个维度上，幂律标度方法失败，临界无序难以确定。此外，在正方形晶格上的刻面的存在产生在小尺度下依赖于晶格的雪崩。我们提出了两种方法，我们发现解决这些问题。首先，我们在Voronoi晶格上进行大规模模拟，以减轻刻面的影响。其次，利用我们最近的重整化群规范形理论，可以直接确定进行标度坍缩所需的普适标度函数的不变自变量。这种方法已被证明是有用的，在干净地捕捉复杂的行为，发生在下和上临界尺寸的系统，并在这里捕捉2D NE-Righting行为很好。所获得的缩放崩溃跨越的范围内的一个因素的混乱和一个因素的$10^4$的雪崩截止。他们是一致的临界无序在零和一个较低的临界尺寸等于2的模型。
英文摘要：
The non-equilibrium random-field Ising model is well studied, yet there are outstanding questions. In two dimensions, power law scaling approaches fail and the critical disorder is difficult to pin down. Additionally, the presence of faceting on the square lattice creates avalanches that are lattice dependent at small scales. We propose two methods which we find solve these issues. First, we perform large scale simulations on a Voronoi lattice to mitigate the effects of faceting. Secondly, the invariant arguments of the universal scaling functions necessary to perform scaling collapses can be directly determined using our recent normal form theory of the Renormalization Group. This method has proven useful in cleanly capturing the complex behavior which occurs in both the lower and upper critical dimensions of systems and here captures the 2D NE-RFIM behavior well. The obtained scaling collapses span over a range of a factor of ten in the disorder and a factor of $10^4$ in avalanche cutoff. They are consistent with a critical disorder at zero and with a lower critical dimension for the model equal to two.
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