In the X-Q model the Néel-VBS transition is strongly first-order for N>2 because the X term cannot generate enough U(1) fluctuations of the dimer pattern.
Georgi,Lie Algebras in Particle Physics: From Isospin to Unified Theories, 2nd ed., Frontiers in Physics, Vol
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SU($N$) Quantum Spin Model with Weak and Strong First-Order N\'eel to Valence-Bond Solid Transitions
In the X-Q model the Néel-VBS transition is strongly first-order for N>2 because the X term cannot generate enough U(1) fluctuations of the dimer pattern.