We study the localization properties of generalized two- and three-dimensional Lieb lattices, ${\mathcal{L}}_2\left(n\right)$ and ${\mathcal{L}}_3\left(n\right)$, $n=1,2,3$ and 4, at energies corresponding to flat and dispersive bands using the transfer matrix method (TMM) and finite size scaling (FSS). We find that the scaling properties of the flat bands are different from scaling in dispersive bands for all ${\mathcal{L}}_d\left(n\right)$. For the $d=3$ dimensional case, states are extended for disorders $W$ down to $W=0.01t$ at the flat bands, indicating that the disorder can lift the degeneracy of the flat bands quickly. The phase diagram with periodic boundary condition for ${\mathcal{L}}_3\left(1\right)$ looks similar to the one for hard boundaries (Liu etal., 2020). We present the critical disorder $W_c$ at energy $E=0$ and find a decreasing $W_c$ for increasing $n$ for ${\mathcal{L}}_3\left(n\right)$, up to $n=3$. Last, we show a table of FSS parameters including so-called irrelevant variables; but the results indicate that the accuracy is too low to determine these reliably.

我们研究了广义二维和三维 Lieb 格的定位特性， ${\mathcal{升}}_2\left(n\right)$ 和 ${\mathcal{升}}_3\left(n\right)$, $n=1,2,3$和 4，在对应于使用传递矩阵方法 (TMM) 和有限尺寸缩放 (FSS) 的平坦和色散带的能量处。我们发现平带的标度特性与色散带的标度不同。 ${\mathcal{升}}_d\left(n\right)$. 为了 $d=3$ 维度案例，状态扩展为障碍 $宽$ 向下 $宽=0.01吨$在平带处，表明无序可以快速解除平带的退化。具有周期性边界条件的相图 ${\mathcal{升}}_3\left(1\right)$看起来类似于硬边界（Liu 等人，2020）。我们提出了严重障碍 ${宽}_C$ 在能源 $乙=0$ 并找到一个递减 ${宽}_C$ 为了增加 $n$ 为了 ${\mathcal{升}}_3\left(n\right)$， 取决于 $n=3$. 最后，我们展示了一个包含所谓不相关变量的 FSS 参数表；但结果表明准确度太低，无法可靠地确定这些。