论文标题
Treelike晶格的表面生长和KPZ类的上部临界维度
Surface growth on treelike lattices and the upper critical dimension of the KPZ class
论文作者
论文摘要
旨在调查[EPL 103（2013）10005]中的KPZ类的上层临界维度，$ d_U $，使用Cayley Trees（CTS）作为基板进行了数值分析，作为基质，以访问其在无限型限制中的行为，并报告了一些意外的结果：logarithmic scaliThmic Inders grouds couds earge earge extrips ex n scrougn ex ex n scrips n s nifter kp（kp）（kp extrips extrips）（kp） $ d = \ infty $ kpz非线性仍然相关）；除了EW类的上部临界维度上方，渐近粗糙的EW表面以外。在这些奇怪的发现中，我在这里重新审视了这些增长模型，以表明这种结果是边界效应的简单后果，这是CTS定义的系统所固有的。实际上，我证明，CT的异常边界会导致不断增长的表面发展弯曲形状，这解释了以前在上述研究中为非平板表面分析了全局“粗糙度”，这解释了先前发现的这些系统的奇怪行为。重要的是，通过测量CT中心部位的高度波动，可以看作是伯特晶格的近似值，对于EW和KPZ类都可以找到光滑的表面，始终如一，始终如一地与尺寸增长的系统预期的行为$ d \ geQslant d_u $。一般，还讨论了1-PT高度波动的有趣特征，例如在稳态状态下不饱和的可能性。
Aiming to investigate the upper critical dimension, $d_u$, of the KPZ class, in [EPL 103 (2013) 10005] some growth models were numerically analyzed using Cayley trees (CTs) as substrates, as a way to access their behavior in the infinite-dimensional limit, and some unexpected results were reported: logarithmic roughness scaling, differing for EW and KPZ models (indicating that even at $d=\infty$ the KPZ nonlinearity is still relevant); beyond asymptotically rough EW surfaces above the upper critical dimension of the EW class. Motivated by these strange findings, I revisit these growth models here to show that such results are simple consequences of boundary effects, inherent to systems defined on CTs. In fact, I demonstrate that the anomalous boundary of the CT leads the growing surfaces to develop curved shapes, which explains the strange behaviors previously found for these systems, once the global "roughness" were analyzed for non-flat surfaces in the study above. Importantly, by measuring the height fluctuations at the central site of the CT, which can be seen as an approximation for the Bethe lattice, smooth surfaces are found for both EW and KPZ classes, consistently with the behavior expected for growing systems in dimensions $d \geqslant d_u$. Interesting features of the 1-pt height fluctuations, such as the possibility of non-saturation in the steady state regime, are also discussed for substrates in general.
