The quantum J₁--J₁'--J₂ spin-1 Heisenberg model: Influence of the interchain coupling on the ground-state magnetic ordering in 2D

We study the phase diagram of the isotropic $J_{1}$--$J_{1}'$--$J_{2}$ Heisenberg model for spin-1 particles on an anisotropic square lattice, using the coupled cluster method. We find no evidence for an intermediate phase between the N\'{e}el and stripe states, as compared with all previous results for the corresponding spin-1/2 case. However, we find a quantum tricritical point at $J_{1}'/J_{1} \approx0.66 \pm 0.03$, $J_{2}/J_{1} \approx0.35\pm0.02$, where a line of second-order phase transitions between the quasi-classical N\'{e}el and stripe-ordered phases (for $J_{1}'/J_{1} \lesssim 0.66$) meets a line of first-order phase transitions between the same two states (for $J_{1}'/J_{1} \gtrsim 0.66$)