Spin-$S$ bilayer Heisenberg models (nearest-neighbor square-lattice antiferromagnets in each layer, with antiferromagnetic interlayer couplings) are treated using dimer mean-field theory for general $S$ and high-order expansions about the dimer limit for $S=1,3/2,\dots ,4\mathrm{}$. We suggest that the transition between the dimer phase at weak intraplane coupling and the Néel phase at strong intraplane coupling is continuous for all $S$, contrary to a recent suggestion based on Schwinger boson mean-field theory. We also present results for $S=1\mathrm{}$ layers based on expansions about the Ising limit: In every respect the $S=1\mathrm{}$ bilayers appear to behave like $S=1/2\mathrm{}$ bilayers, further supporting our picture for the nature of the order-disorder phase transition.

• Received 23 May 1997

DOI:https://doi.org/10.1103/PhysRevB.57.392