Phase Transitions of the Bilayered Spin-S Heisenberg Model and Its Extension to Fractional Dimensions

We study the ground state and the phase transitions of the bilayered spin-$S$ antiferromagnetic Heisenberg model using the Schwinger boson mean field theory. The interplane coupling initially stabilizes but eventually destroys the long-range antiferromagnetic order. The transition to the disordered state is continuous for small $S$, and first order for large $S$. The latter is consistent with an argument based on the spin wave theory. The phase diagram and phase transitions in corresponding model in fractional dimensions are also discussed.