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 $J_{ 1}'/J_{ 1} \gtrsim 0.66$)
Categories: cond-mat.str-el