摘要翻译：
我们数值研究了各种界面生长模型粗糙度分布的标度关系中的有限尺寸修正。对于一组2+1维的类弹道模型，即使考虑了很大的系统尺寸，也不服从以平均粗糙度<W_2>$为标度因子的最常见的关系式。另一方面，用包含粗糙度均方根涨落的标度关系，可以用标度函数二阶矩的有限尺寸效应来解释，得到相同数据的良好崩塌。我们还用一个替代的缩放关系得到了数据折叠，该关系考虑了本征宽度的影响，本征宽度是以前为$<W_2>$的缩放提出的一个常数校正项。这说明了如何从粗糙度分布缩放中获得有限尺寸的校正。然而，我们通过分析相邻柱之间不同最大高度差的有限实-实模型的数据，抛弃了固有宽度是高表面台阶的结果的通常解释。我们还观察到，粗糙度分布的大的有限尺寸修正通常伴随着高度分布和平均局部斜率的大修正，以及标度指数的估计。Das、Sarma和Tamborenea在1+1维的分子束外延模型是一个例子，其中所提出的标度关系都不正确，而其他测量量都不收敛于期望的渐近值。因此，尽管粗糙度分布显然比其他量更好地确定一个增长系统的普遍性类别，但它不是这项任务的最终解决方案。
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英文标题：
《Finite-size effects in roughness distribution scaling》
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作者：
T. J. Oliveira and F. D. A. Aarao Reis
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最新提交年份：
2008
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  We study numerically finite-size corrections in scaling relations for roughness distributions of various interface growth models. The most common relation, which considers the average roughness $<w_2>$ as scaling factor, is not obeyed in the steady states of a group of ballistic-like models in 2+1 dimensions, even when very large system sizes are considered. On the other hand, good collapse of the same data is obtained with a scaling relation that involves the root mean square fluctuation of the roughness, which can be explained by finite-size effects on second moments of the scaling functions. We also obtain data collapse with an alternative scaling relation that accounts for the effect of the intrinsic width, which is a constant correction term previously proposed for the scaling of $<w_2>$. This illustrates how finite-size corrections can be obtained from roughness distributions scaling. However, we discard the usual interpretation that the intrinsic width is a consequence of high surface steps by analyzing data of restricted solid-on-solid models with various maximal height differences between neighboring columns. We also observe that large finite-size corrections in the roughness distributions are usually accompanied by huge corrections in height distributions and average local slopes, as well as in estimates of scaling exponents. The molecular-beam epitaxy model of Das Sarma and Tamborenea in 1+1 dimensions is a case example in which none of the proposed scaling relations works properly, while the other measured quantities do not converge to the expected asymptotic values. Thus, although roughness distributions are clearly better than other quantities to determine the universality class of a growing system, it is not the final solution for this task.
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PDF链接：
https://arxiv.org/pdf/706.1307