Schwinger-Boson Mean Field Solution of Spin-1 (or 1/2) 2D Anisotropic Heisenberg Antiferromagnet

Using the Resonant Valence Bond (RVB) concept and the Schwinger-boson mean field approximation, we investigate a two dimensional anisotropic Heisenberg antiferromagnet. We find that increasing the coupling ratio ($\alpha =J_y\mathrm{/}{J}_x$), a disordered-ordered phase transition appears beyond a critical value (${\alpha }_c$). When $\alpha >{\alpha }_c$ there exists a finite $T_N$ beyond which an ordered-disordered phase transition occurs, while for $\alpha <{\alpha }_c$ there always exists a gap. Also we find that a decoupling temperature $T_D$ exists for 1D and 2D isotropic case, when $T$ approaches $T_D$ the RVB order parameter decreases rapidly to zero.