Order-disorder transitions in bilayer Heisenberg models on the triangular lattice

The triangular-lattice bilayer Heisenberg model with antiferromagnetic inte rlayer coupling J(0) is studied using strong-coupling perturbation theory a nd bond-operator mean-field theory. It is found that the model with ferroma gnetic intralayer coupling J<0 undergoes a quantum order-disorder transitio n at a strong-J(0) critical point J(0c) = 3.83J. While for the model with J >0, the transition point is very small, J(0c)=0.15J. The result implies tha t the single-layer triangular Heisenberg antiferromagnet only has small lon g-range order parameter (if ordered) so that it is very sensitive to the in terlayer perturbation.