  The Hamiltonian of a two-sublattice antiferromagnetic spins, with single
(hard-axis) and double ion anisotropies described by $H=J
\bold{\hat{S}}_{1}\cdot\bold{\hat{S}}_{2} -
2J_{z}\hat{S}_{1z}\hat{S}_{2z}+K(\hat{S}_{1z}^2 +\hat{S}_{2z}^2)$ is
investigated using the method of effective potential. The problem is mapped to
a single particle quantum-mechanical Hamiltonian in terms of the relative
coordinate and reduced mass. We study the quantum-classical phase transition of
the escape rate of this model. We show that the first-order phase transition
for this model sets in at the critical value $J_c=\frac{K+J_z}{2}$ while for
the anisotropic Heisenberg coupling $H = J(S_{1x}S_{2x} +S_{1y}S_{2y}) +
J_zS_{1z}S_{2z} + K(S_{1z}^2+ S_{2z}^2)$ we obtain $J_c=\frac{2K-J_z}{3}$ . The
phase diagrams of the transition are also studied.
