  We study the spin-1/2 $J_{1}$-$J_{2}$ Heisenberg model on a square lattice
using the cluster mean-field theory. We find a rapid convergence of phase
boundaries with increasing cluster size. By extrapolating the cluster size $L$
to infinity, we obtain accurate phase boundaries $J_{2}^{c1} \approx 0.42$
(between the N$\acute{e}$el antiferromagnetic phase and nonmagnetic phase), and
$J_{2}^{c2} \approx 0.59$ (between nonmagnetic phase and the collinear
antiferromagnetic phase). The transitions are identified unambiguously as
second order at $J_{2}^{c1}$ and first order at $J_{2}^{c2}$. At finite
temperature, we present a complete phase diagram with stable, meta-stable and
unstable states near $J_{2}^{c2}$, being relevant to that of the anisotropic
$J_1-J_2$ model. The uniform as well as staggered magnetic susceptibilities are
also discussed.
