  We estimate phase boundaries of four ordered and two spin-liquid phases for
the spin-$\frac{1}{2}$ Kitaev-Heisenberg (KH) model using four kinds of
relatively-small clusters, based on the second derivative of ground-state
energy. The estimated values are compared between the clusters as well as the
previous iPEPS results. We thus find that the boundaries can be accurately
estimated within limited-size clusters. The used clusters may appropriate to
study higher-$S$ KH models having less fluctuations.
