The quantum $J_1$--$J_1^{\mathrm{\prime }}$--$J_2$ 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 $J_1$–$J_1^{\mathrm{\prime }}$–$J_2$ 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 $J_1^{\mathrm{\prime }}\mathrm{/}{J}_1\approx 0.66\pm 0.03$, $J_2\mathrm{/}{J}_1\approx 0.35\pm 0.02$, where a line of second-order phase transitions between the quasi-classical N'{e}el and stripe-ordered phases (for $J_1^{\mathrm{\prime }}\mathrm{/}{J}_1\lesssim 0.66$) meets a line of first-order phase transitions between the same two states (for $J_1^{\mathrm{\prime }}\mathrm{/}{J}_1\gtrsim 0.66$)