  Ground-state properties of the two-dimensional $S=1/2$ random Heisenberg
models are investigated by the exact-diagonalization method. The phase diagram
of the bond-random model (the $\pm J$ model) is the same as that of the
corresponding Ising spin glass model, in spite of quantum fluctuation. In the
site-random model, the spin glass phase exists at least in the ferro-rich case.
In comparison with the corresponding Ising model, the N\'eel phase of this
model becomes much narrower in the ferro-rich case, while it is comparable in
the antiferro-rich case.
  KEYWORDS: quantum spin glass, Heisenberg model, ground-state phase
transition, site-random model, exact diagonalization
