Figure 2: Quantum zero point energy and the magnetic order.

We have chosen the representative parameters in regions I and III with D=0.2J, J′=0.6J in (a) and D=0.05J, J′=0.6J in (c), respectively. (b) The magnetic order in regions I and II with θ=π/2 and the spins pointing along the local . (d) The magnetic order in region III with θ=0 and the spins pointing along the local
.