1. Could the authors clarify (for completeness) what is meant by the decoupled Ising model.
2. The long sentence starting just above 1.2 and finishing after 1.3 could be improved a bit in clarity.
3. In 2.1, it's a bit odd at first to say that $\phi_i$ lives in the off-diagonal irrep when this has just been explained as coming from a piece of the symmetric traceless tensor, in the sense that one expects that $\phi_i$ should be coming from the fundamental of O(3). I'm guessing the fundamental of O(3) turns out to transform in the same irrep thanks to eqn. 2.3? If so, might be worth making this more explicit.
4. In 2.7, it is not obvious what irrep $Y'_l$ belongs to, given the notation up to that point. Perhaps the Z in 2.3 could be changed to a Y with a single index, or the Y in 2.7 could be changed to a Z?
5. It would be important for the authors to comment on the dependence of their numerical results on the gap assumption on $\phi'$.
6. It would be useful, if possible, to place the eps-expansion cubic fixed point on the exclusion plots.